J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 2 3 | 1 2 3 | | 1 2 3 | 1 2 3 | 2 | 1 2 3 | 1 2 3 | | A | 4 5 6 | 4 5 6 | 4 | 4 5 6 | 4 5 6 | | 4 5 6 | 4 5 6 | 5 | | 7 8 9 | 7 8 9 | | 7 8 9 | 7 8 9 | | 7 8 9 | 7 8 9 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 2 3 | 1 2 3 | 1 2 3 | | 1 2 3 | 1 2 3 | 1 2 3 | | 1 2 3 | B | 4 5 6 | 4 5 6 | 4 5 6 | | 4 5 6 | 4 5 6 | 4 5 6 | 4 | 4 5 6 | | 7 8 9 | 7 8 9 | 7 8 9 | 8 | 7 8 9 | 7 8 9 | 7 8 9 | | 7 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 1 2 3 | 1 2 3 | 1 2 3 | | 1 2 3 | | 1 2 3 | 1 2 3 | C | | 4 5 6 | 4 5 6 | 4 5 6 | 5 | 4 5 6 | 6 | 4 5 6 | 4 5 6 | | | 7 8 9 | 7 8 9 | 7 8 9 | | 7 8 9 | | 7 8 9 | 7 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 2 3 | 3 | | 1 2 3 | 1 2 3 | | 1 2 3 | 1 2 3 | 1 2 3 | D | 4 5 6 | | | 4 5 6 | 4 5 6 | | 4 5 6 | 4 5 6 | 4 5 6 | | 7 8 9 | | 7 | 7 8 9 | 7 8 9 | 8 | 7 8 9 | 7 8 9 | 7 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 2 | E | | 4 5 6 | 4 5 6 | 4 5 6 | 4 5 6 | 4 5 6 | 4 5 6 | 4 5 6 | | | 8 | 7 8 9 | 7 8 9 | 7 8 9 | 7 8 9 | 7 8 9 | 7 8 9 | 7 8 9 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 2 3 | 1 2 3 | 1 2 3 | | 1 2 3 | 1 2 3 | 1 | | 1 2 3 | F | 4 5 6 | 4 5 6 | 4 5 6 | 6 | 4 5 6 | 4 5 6 | | | 4 5 6 | | 7 8 9 | 7 8 9 | 7 8 9 | | 7 8 9 | 7 8 9 | | 9 | 7 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 2 3 | 1 2 3 | 2 | 1 2 3 | | 1 2 3 | 1 2 3 | 1 2 3 | | G | 4 5 6 | 4 5 6 | | 4 5 6 | | 4 5 6 | 4 5 6 | 4 5 6 | | | 7 8 9 | 7 8 9 | | 7 8 9 | 9 | 7 8 9 | 7 8 9 | 7 8 9 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 2 3 | | 1 2 3 | 1 2 3 | 1 2 3 | | 1 2 3 | 1 2 3 | 1 2 3 | H | 4 5 6 | | 4 5 6 | 4 5 6 | 4 5 6 | 5 | 4 5 6 | 4 5 6 | 4 5 6 | | 7 8 9 | 7 | 7 8 9 | 7 8 9 | 7 8 9 | | 7 8 9 | 7 8 9 | 7 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 2 3 | 1 2 3 | | 1 2 3 | 1 2 3 | 3 | 1 2 3 | 1 2 3 | I | 6 | 4 5 6 | 4 5 6 | 4 | 4 5 6 | 4 5 6 | | 4 5 6 | 4 5 6 | | | 7 8 9 | 7 8 9 | | 7 8 9 | 7 8 9 | | 7 8 9 | 7 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 72 Deductions found: 1. Since {(There is something in AL)} we know 1 of {4AL} are true. But those are a subset of {(There is a 4 in row A)}. Therefore, we know that none of {4AJ or 4AK or 4AM or 4AN or 4AP or 4AQ} are true. 2. Since {(There is something in AL)} we know 1 of {4AL} are true. But those are a subset of {(There is a 4 in column L)}. Therefore, we know that none of {4BL or 4CL or 4EL or 4FL or 4HL or 4IL} are true. 3. Since {(There is something in AL)} we know 1 of {4AL} are true. But those are a subset of {(There is a 4 in box 1)}. Therefore, we know that none of {4AJ or 4AK or 4BJ or 4BK or 4BL or 4CK or 4CL} are true. 4. Since {(There is something in AO)} we know 1 of {2AO} are true. But those are a subset of {(There is a 2 in row A)}. Therefore, we know that none of {2AJ or 2AK or 2AM or 2AN or 2AP or 2AQ} are true. 5. Since {(There is something in AO)} we know 1 of {2AO} are true. But those are a subset of {(There is a 2 in column O)}. Therefore, we know that none of {2BO or 2CO or 2EO or 2FO or 2GO or 2IO} are true. 6. Since {(There is something in AO)} we know 1 of {2AO} are true. But those are a subset of {(There is a 2 in box 2)}. Therefore, we know that none of {2AM or 2AN or 2BN or 2BO or 2CM or 2CO} are true. 7. Since {(There is something in AR)} we know 1 of {5AR} are true. But those are a subset of {(There is a 5 in row A)}. Therefore, we know that none of {5AJ or 5AK or 5AM or 5AN or 5AP or 5AQ} are true. 8. Since {(There is something in AR)} we know 1 of {5AR} are true. But those are a subset of {(There is a 5 in column R)}. Therefore, we know that none of {5BR or 5CR or 5DR or 5FR or 5HR or 5IR} are true. 9. Since {(There is something in AR)} we know 1 of {5AR} are true. But those are a subset of {(There is a 5 in box 3)}. Therefore, we know that none of {5AP or 5AQ or 5BP or 5BR or 5CQ or 5CR} are true. 10. Since {(There is something in BM)} we know 1 of {8BM} are true. But those are a subset of {(There is a 8 in row B)}. Therefore, we know that none of {8BJ or 8BK or 8BL or 8BN or 8BO or 8BP or 8BR} are true. 11. Since {(There is something in BM)} we know 1 of {8BM} are true. But those are a subset of {(There is a 8 in column M)}. Therefore, we know that none of {8AM or 8CM or 8DM or 8EM or 8GM or 8HM} are true. 12. Since {(There is something in BM)} we know 1 of {8BM} are true. But those are a subset of {(There is a 8 in box 2)}. Therefore, we know that none of {8AM or 8AN or 8BN or 8BO or 8CM or 8CO} are true. 13. Since {(There is something in BQ)} we know 1 of {4BQ} are true. But those are a subset of {(There is a 4 in row B)}. Therefore, we know that none of {4BJ or 4BK or 4BL or 4BN or 4BO or 4BP or 4BR} are true. 14. Since {(There is something in BQ)} we know 1 of {4BQ} are true. But those are a subset of {(There is a 4 in column Q)}. Therefore, we know that none of {4AQ or 4CQ or 4DQ or 4EQ or 4GQ or 4HQ or 4IQ} are true. 15. Since {(There is something in BQ)} we know 1 of {4BQ} are true. But those are a subset of {(There is a 4 in box 3)}. Therefore, we know that none of {4AP or 4AQ or 4BP or 4BR or 4CQ or 4CR} are true. 16. Since {(There is something in CJ)} we know 1 of {1CJ} are true. But those are a subset of {(There is a 1 in row C)}. Therefore, we know that none of {1CK or 1CL or 1CM or 1CO or 1CQ or 1CR} are true. 17. Since {(There is something in CJ)} we know 1 of {1CJ} are true. But those are a subset of {(There is a 1 in column J)}. Therefore, we know that none of {1AJ or 1BJ or 1DJ or 1FJ or 1GJ or 1HJ} are true. 18. Since {(There is something in CJ)} we know 1 of {1CJ} are true. But those are a subset of {(There is a 1 in box 1)}. Therefore, we know that none of {1AJ or 1AK or 1BJ or 1BK or 1BL or 1CK or 1CL} are true. 19. Since {(There is something in CN)} we know 1 of {5CN} are true. But those are a subset of {(There is a 5 in row C)}. Therefore, we know that none of {5CK or 5CL or 5CM or 5CO or 5CQ or 5CR} are true. 20. Since {(There is something in CN)} we know 1 of {5CN} are true. But those are a subset of {(There is a 5 in column N)}. Therefore, we know that none of {5AN or 5BN or 5DN or 5EN or 5FN or 5HN or 5IN} are true. 21. Since {(There is something in CN)} we know 1 of {5CN} are true. But those are a subset of {(There is a 5 in box 2)}. Therefore, we know that none of {5AM or 5AN or 5BN or 5BO or 5CM or 5CO} are true. 22. Since {(There is something in CP)} we know 1 of {6CP} are true. But those are a subset of {(There is a 6 in row C)}. Therefore, we know that none of {6CK or 6CL or 6CM or 6CO or 6CQ or 6CR} are true. 23. Since {(There is something in CP)} we know 1 of {6CP} are true. But those are a subset of {(There is a 6 in column P)}. Therefore, we know that none of {6AP or 6BP or 6DP or 6EP or 6GP or 6HP} are true. 24. Since {(There is something in CP)} we know 1 of {6CP} are true. But those are a subset of {(There is a 6 in box 3)}. Therefore, we know that none of {6AP or 6AQ or 6BP or 6BR or 6CQ or 6CR} are true. 25. Since {(There is something in DK)} we know 1 of {3DK} are true. But those are a subset of {(There is a 3 in row D)}. Therefore, we know that none of {3DJ or 3DM or 3DN or 3DP or 3DQ or 3DR} are true. 26. Since {(There is something in DK)} we know 1 of {3DK} are true. But those are a subset of {(There is a 3 in column K)}. Therefore, we know that none of {3AK or 3BK or 3CK or 3EK or 3FK or 3GK or 3IK} are true. 27. Since {(There is something in DK)} we know 1 of {3DK} are true. But those are a subset of {(There is a 3 in box 4)}. Therefore, we know that none of {3DJ or 3EK or 3EL or 3FJ or 3FK or 3FL} are true. 28. Since {(There is something in DL)} we know 1 of {7DL} are true. But those are a subset of {(There is a 7 in row D)}. Therefore, we know that none of {7DJ or 7DM or 7DN or 7DP or 7DQ or 7DR} are true. 29. Since {(There is something in DL)} we know 1 of {7DL} are true. But those are a subset of {(There is a 7 in column L)}. Therefore, we know that none of {7BL or 7CL or 7EL or 7FL or 7HL or 7IL} are true. 30. Since {(There is something in DL)} we know 1 of {7DL} are true. But those are a subset of {(There is a 7 in box 4)}. Therefore, we know that none of {7DJ or 7EK or 7EL or 7FJ or 7FK or 7FL} are true. 31. Since {(There is something in DO)} we know 1 of {8DO} are true. But those are a subset of {(There is a 8 in row D)}. Therefore, we know that none of {8DJ or 8DM or 8DN or 8DP or 8DQ or 8DR} are true. 32. Since {(There is something in DO)} we know 1 of {8DO} are true. But those are a subset of {(There is a 8 in column O)}. Therefore, we know that none of {8BO or 8CO or 8EO or 8FO or 8GO or 8IO} are true. 33. Since {(There is something in DO)} we know 1 of {8DO} are true. But those are a subset of {(There is a 8 in box 5)}. Therefore, we know that none of {8DM or 8DN or 8EM or 8EN or 8EO or 8FN or 8FO} are true. 34. Since {(There is something in EJ)} we know 1 of {8EJ} are true. But those are a subset of {(There is a 8 in row E)}. Therefore, we know that none of {8EK or 8EL or 8EM or 8EN or 8EO or 8EP or 8EQ} are true. 35. Since {(There is something in EJ)} we know 1 of {8EJ} are true. But those are a subset of {(There is a 8 in column J)}. Therefore, we know that none of {8AJ or 8BJ or 8DJ or 8FJ or 8GJ or 8HJ} are true. 36. Since {(There is something in EJ)} we know 1 of {8EJ} are true. But those are a subset of {(There is a 8 in box 4)}. Therefore, we know that none of {8DJ or 8EK or 8EL or 8FJ or 8FK or 8FL} are true. 37. Since {(There is something in ER)} we know 1 of {2ER} are true. But those are a subset of {(There is a 2 in row E)}. Therefore, we know that none of {2EK or 2EL or 2EM or 2EN or 2EO or 2EP or 2EQ} are true. 38. Since {(There is something in ER)} we know 1 of {2ER} are true. But those are a subset of {(There is a 2 in column R)}. Therefore, we know that none of {2BR or 2CR or 2DR or 2FR or 2HR or 2IR} are true. 39. Since {(There is something in ER)} we know 1 of {2ER} are true. But those are a subset of {(There is a 2 in box 6)}. Therefore, we know that none of {2DP or 2DQ or 2DR or 2EP or 2EQ or 2FR} are true. 40. Since {(There is something in FM)} we know 1 of {6FM} are true. But those are a subset of {(There is a 6 in row F)}. Therefore, we know that none of {6FJ or 6FK or 6FL or 6FN or 6FO or 6FR} are true. 41. Since {(There is something in FM)} we know 1 of {6FM} are true. But those are a subset of {(There is a 6 in column M)}. Therefore, we know that none of {6AM or 6CM or 6DM or 6EM or 6GM or 6HM} are true. 42. Since {(There is something in FM)} we know 1 of {6FM} are true. But those are a subset of {(There is a 6 in box 5)}. Therefore, we know that none of {6DM or 6DN or 6EM or 6EN or 6EO or 6FN or 6FO} are true. 43. Since {(There is something in FP)} we know 1 of {1FP} are true. But those are a subset of {(There is a 1 in row F)}. Therefore, we know that none of {1FJ or 1FK or 1FL or 1FN or 1FO or 1FR} are true. 44. Since {(There is something in FP)} we know 1 of {1FP} are true. But those are a subset of {(There is a 1 in column P)}. Therefore, we know that none of {1AP or 1BP or 1DP or 1EP or 1GP or 1HP} are true. 45. Since {(There is something in FP)} we know 1 of {1FP} are true. But those are a subset of {(There is a 1 in box 6)}. Therefore, we know that none of {1DP or 1DQ or 1DR or 1EP or 1EQ or 1FR} are true. 46. Since {(There is something in FQ)} we know 1 of {9FQ} are true. But those are a subset of {(There is a 9 in row F)}. Therefore, we know that none of {9FJ or 9FK or 9FL or 9FN or 9FO or 9FR} are true. 47. Since {(There is something in FQ)} we know 1 of {9FQ} are true. But those are a subset of {(There is a 9 in column Q)}. Therefore, we know that none of {9AQ or 9CQ or 9DQ or 9EQ or 9GQ or 9HQ or 9IQ} are true. 48. Since {(There is something in FQ)} we know 1 of {9FQ} are true. But those are a subset of {(There is a 9 in box 6)}. Therefore, we know that none of {9DP or 9DQ or 9DR or 9EP or 9EQ or 9FR} are true. 49. Since {(There is something in GL)} we know 1 of {2GL} are true. But those are a subset of {(There is a 2 in row G)}. Therefore, we know that none of {2GJ or 2GK or 2GM or 2GO or 2GP or 2GQ} are true. 50. Since {(There is something in GL)} we know 1 of {2GL} are true. But those are a subset of {(There is a 2 in column L)}. Therefore, we know that none of {2BL or 2CL or 2EL or 2FL or 2HL or 2IL} are true. 51. Since {(There is something in GL)} we know 1 of {2GL} are true. But those are a subset of {(There is a 2 in box 7)}. Therefore, we know that none of {2GJ or 2GK or 2HJ or 2HL or 2IK or 2IL} are true. 52. Since {(There is something in GN)} we know 1 of {9GN} are true. But those are a subset of {(There is a 9 in row G)}. Therefore, we know that none of {9GJ or 9GK or 9GM or 9GO or 9GP or 9GQ} are true. 53. Since {(There is something in GN)} we know 1 of {9GN} are true. But those are a subset of {(There is a 9 in column N)}. Therefore, we know that none of {9AN or 9BN or 9DN or 9EN or 9FN or 9HN or 9IN} are true. 54. Since {(There is something in GN)} we know 1 of {9GN} are true. But those are a subset of {(There is a 9 in box 8)}. Therefore, we know that none of {9GM or 9GO or 9HM or 9HN or 9IN or 9IO} are true. 55. Since {(There is something in GR)} we know 1 of {7GR} are true. But those are a subset of {(There is a 7 in row G)}. Therefore, we know that none of {7GJ or 7GK or 7GM or 7GO or 7GP or 7GQ} are true. 56. Since {(There is something in GR)} we know 1 of {7GR} are true. But those are a subset of {(There is a 7 in column R)}. Therefore, we know that none of {7BR or 7CR or 7DR or 7FR or 7HR or 7IR} are true. 57. Since {(There is something in GR)} we know 1 of {7GR} are true. But those are a subset of {(There is a 7 in box 9)}. Therefore, we know that none of {7GP or 7GQ or 7HP or 7HQ or 7HR or 7IQ or 7IR} are true. 58. Since {(There is something in HK)} we know 1 of {7HK} are true. But those are a subset of {(There is a 7 in row H)}. Therefore, we know that none of {7HJ or 7HL or 7HM or 7HN or 7HP or 7HQ or 7HR} are true. 59. Since {(There is something in HK)} we know 1 of {7HK} are true. But those are a subset of {(There is a 7 in column K)}. Therefore, we know that none of {7AK or 7BK or 7CK or 7EK or 7FK or 7GK or 7IK} are true. 60. Since {(There is something in HK)} we know 1 of {7HK} are true. But those are a subset of {(There is a 7 in box 7)}. Therefore, we know that none of {7GJ or 7GK or 7HJ or 7HL or 7IK or 7IL} are true. 61. Since {(There is something in HO)} we know 1 of {5HO} are true. But those are a subset of {(There is a 5 in row H)}. Therefore, we know that none of {5HJ or 5HL or 5HM or 5HN or 5HP or 5HQ or 5HR} are true. 62. Since {(There is something in HO)} we know 1 of {5HO} are true. But those are a subset of {(There is a 5 in column O)}. Therefore, we know that none of {5BO or 5CO or 5EO or 5FO or 5GO or 5IO} are true. 63. Since {(There is something in HO)} we know 1 of {5HO} are true. But those are a subset of {(There is a 5 in box 8)}. Therefore, we know that none of {5GM or 5GO or 5HM or 5HN or 5IN or 5IO} are true. 64. Since {(There is something in IJ)} we know 1 of {6IJ} are true. But those are a subset of {(There is a 6 in row I)}. Therefore, we know that none of {6IK or 6IL or 6IN or 6IO or 6IQ or 6IR} are true. 65. Since {(There is something in IJ)} we know 1 of {6IJ} are true. But those are a subset of {(There is a 6 in column J)}. Therefore, we know that none of {6AJ or 6BJ or 6DJ or 6FJ or 6GJ or 6HJ} are true. 66. Since {(There is something in IJ)} we know 1 of {6IJ} are true. But those are a subset of {(There is a 6 in box 7)}. Therefore, we know that none of {6GJ or 6GK or 6HJ or 6HL or 6IK or 6IL} are true. 67. Since {(There is something in IM)} we know 1 of {4IM} are true. But those are a subset of {(There is a 4 in row I)}. Therefore, we know that none of {4IK or 4IL or 4IN or 4IO or 4IQ or 4IR} are true. 68. Since {(There is something in IM)} we know 1 of {4IM} are true. But those are a subset of {(There is a 4 in column M)}. Therefore, we know that none of {4AM or 4CM or 4DM or 4EM or 4GM or 4HM} are true. 69. Since {(There is something in IM)} we know 1 of {4IM} are true. But those are a subset of {(There is a 4 in box 8)}. Therefore, we know that none of {4GM or 4GO or 4HM or 4HN or 4IN or 4IO} are true. 70. Since {(There is something in IP)} we know 1 of {3IP} are true. But those are a subset of {(There is a 3 in row I)}. Therefore, we know that none of {3IK or 3IL or 3IN or 3IO or 3IQ or 3IR} are true. 71. Since {(There is something in IP)} we know 1 of {3IP} are true. But those are a subset of {(There is a 3 in column P)}. Therefore, we know that none of {3AP or 3BP or 3DP or 3EP or 3GP or 3HP} are true. 72. Since {(There is something in IP)} we know 1 of {3IP} are true. But those are a subset of {(There is a 3 in box 9)}. Therefore, we know that none of {3GP or 3GQ or 3HP or 3HQ or 3HR or 3IQ or 3IR} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 3 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | 7 | | 7 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 5 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | 7 | 7 9 | 7 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | 3 | | 2 3 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | 7 9 | | 7 8 | 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 5 | | | 5 | 4 | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | 9 | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | 1 3 | 1 3 | 1 3 | | 3 | 2 | E | | 4 5 6 | 5 6 | 5 | 4 | 4 | 4 5 | 5 6 | | | 8 | 9 | 9 | 7 9 | 7 | 7 9 | 7 | 7 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | 3 | F | 4 5 | 4 5 | 5 | 6 | 4 | 4 | | | 4 | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | 5 | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in AL) will enslave (There is a 4 in row A) (There is something in AL) will enslave (There is a 4 in column L) (There is something in AL) will enslave (There is a 4 in box 1) (There is something in AO) will enslave (There is a 2 in row A) (There is something in AO) will enslave (There is a 2 in column O) (There is something in AO) will enslave (There is a 2 in box 2) (There is something in AR) will enslave (There is a 5 in row A) (There is something in AR) will enslave (There is a 5 in column R) (There is something in AR) will enslave (There is a 5 in box 3) (There is something in BM) will enslave (There is a 8 in row B) (There is something in BM) will enslave (There is a 8 in column M) (There is something in BM) will enslave (There is a 8 in box 2) (There is something in BQ) will enslave (There is a 4 in row B) (There is something in BQ) will enslave (There is a 4 in column Q) (There is something in BQ) will enslave (There is a 4 in box 3) (There is something in CJ) will enslave (There is a 1 in row C) (There is something in CJ) will enslave (There is a 1 in column J) (There is something in CJ) will enslave (There is a 1 in box 1) (There is something in CN) will enslave (There is a 5 in row C) (There is something in CN) will enslave (There is a 5 in column N) (There is something in CN) will enslave (There is a 5 in box 2) (There is something in CP) will enslave (There is a 6 in row C) (There is something in CP) will enslave (There is a 6 in column P) (There is something in CP) will enslave (There is a 6 in box 3) (There is something in DK) will enslave (There is a 3 in row D) (There is something in DK) will enslave (There is a 3 in column K) (There is something in DK) will enslave (There is a 3 in box 4) (There is something in DL) will enslave (There is a 7 in row D) (There is something in DL) will enslave (There is a 7 in column L) (There is something in DL) will enslave (There is a 7 in box 4) (There is something in DO) will enslave (There is a 8 in row D) (There is something in DO) will enslave (There is a 8 in column O) (There is something in DO) will enslave (There is a 8 in box 5) (There is something in EJ) will enslave (There is a 8 in row E) (There is something in EJ) will enslave (There is a 8 in column J) (There is something in EJ) will enslave (There is a 8 in box 4) (There is something in ER) will enslave (There is a 2 in row E) (There is something in ER) will enslave (There is a 2 in column R) (There is something in ER) will enslave (There is a 2 in box 6) (There is something in FM) will enslave (There is a 6 in row F) (There is something in FM) will enslave (There is a 6 in column M) (There is something in FM) will enslave (There is a 6 in box 5) (There is something in FP) will enslave (There is a 1 in row F) (There is something in FP) will enslave (There is a 1 in column P) (There is something in FP) will enslave (There is a 1 in box 6) (There is something in FQ) will enslave (There is a 9 in row F) (There is something in FQ) will enslave (There is a 9 in column Q) (There is something in FQ) will enslave (There is a 9 in box 6) (There is something in GL) will enslave (There is a 2 in row G) (There is something in GL) will enslave (There is a 2 in column L) (There is something in GL) will enslave (There is a 2 in box 7) (There is something in GN) will enslave (There is a 9 in row G) (There is something in GN) will enslave (There is a 9 in column N) (There is something in GN) will enslave (There is a 9 in box 8) (There is something in GR) will enslave (There is a 7 in row G) (There is something in GR) will enslave (There is a 7 in column R) (There is something in GR) will enslave (There is a 7 in box 9) (There is something in HK) will enslave (There is a 7 in row H) (There is something in HK) will enslave (There is a 7 in column K) (There is something in HK) will enslave (There is a 7 in box 7) (There is something in HO) will enslave (There is a 5 in row H) (There is something in HO) will enslave (There is a 5 in column O) (There is something in HO) will enslave (There is a 5 in box 8) (There is something in IJ) will enslave (There is a 6 in row I) (There is something in IJ) will enslave (There is a 6 in column J) (There is something in IJ) will enslave (There is a 6 in box 7) (There is something in IM) will enslave (There is a 4 in row I) (There is something in IM) will enslave (There is a 4 in column M) (There is something in IM) will enslave (There is a 4 in box 8) (There is something in IP) will enslave (There is a 3 in row I) (There is something in IP) will enslave (There is a 3 in column P) (There is something in IP) will enslave (There is a 3 in box 9) (There is a 5 in row B) will enslave (There is a 5 in box 1) (There is a 4 in row C) will enslave (There is a 4 in box 2) (There is a 8 in row F) will enslave (There is a 8 in box 6) (There is a 7 in row I) will enslave (There is a 7 in box 8) (There is a 7 in column J) will enslave (There is a 7 in box 1) (There is a 5 in column M) will enslave (There is a 5 in box 5) (There is a 8 in column N) will enslave (There is a 8 in box 8) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 3 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | 7 | | 7 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 5 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | 7 | 7 9 | 7 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | 3 | | 2 3 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | 7 9 | | 7 8 | 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 5 | | | 5 | 4 | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | 9 | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | 1 3 | 1 3 | 1 3 | | 3 | 2 | E | | 4 5 6 | 5 6 | 5 | 4 | 4 | 4 5 | 5 6 | | | 8 | 9 | 9 | 7 9 | 7 | 7 9 | 7 | 7 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | 3 | F | 4 5 | 4 5 | 5 | 6 | 4 | 4 | | | 4 | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | 5 | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 8 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 15 Deductions found: 1. Since {(There is a 7 in box 6)} we know 1 of {7EP or 7EQ} are true. But those are a subset of {(There is a 7 in row E)}. Therefore, we know that none of {7EM or 7EN or 7EO} are true. 2. Since {(There is a 6 in box 4)} we know 1 of {6EK or 6EL} are true. But those are a subset of {(There is a 6 in row E)}. Therefore, we know that none of {6EQ} are true. 3. Since {(There is a 1 in box 4)} we know 1 of {1EK or 1EL} are true. But those are a subset of {(There is a 1 in row E)}. Therefore, we know that none of {1EM or 1EN or 1EO} are true. 4. Since {(There is a 4 in column N)} we know 1 of {4DN or 4EN or 4FN} are true. But those are a subset of {(There is a 4 in box 5)}. Therefore, we know that none of {4EO or 4FO} are true. 5. Since {(There is a 8 in row F)} we know 1 of {8FR} are true. But those are a subset of {(There is a 8 in column R)}. Therefore, we know that none of {8CR or 8HR or 8IR} are true. 6. Since {(There is a 8 in row F)} we know 1 of {8FR} are true. But those are a subset of {(There is something in FR)}. Therefore, we know that none of {3FR or 4FR} are true. 7. Since {(There is a 7 in row F)} we know 1 of {7FN or 7FO} are true. But those are a subset of {(There is a 7 in box 5)}. Therefore, we know that none of {7EM or 7EN or 7EO} are true. 8. Since {(There is a 5 in row F)} we know 1 of {5FJ or 5FK or 5FL} are true. But those are a subset of {(There is a 5 in box 4)}. Therefore, we know that none of {5DJ or 5EK or 5EL} are true. 9. Since {(There is a 6 in row D)} we know 1 of {6DQ or 6DR} are true. But those are a subset of {(There is a 6 in box 6)}. Therefore, we know that none of {6EQ} are true. 10. Since {(There is a 1 in row D)} we know 1 of {1DM or 1DN} are true. But those are a subset of {(There is a 1 in box 5)}. Therefore, we know that none of {1EM or 1EN or 1EO} are true. 11. Since {(There is a 4 in row C)} we know 1 of {4CO} are true. But those are a subset of {(There is a 4 in column O)}. Therefore, we know that none of {4EO or 4FO} are true. 12. Since {(There is a 4 in row C)} we know 1 of {4CO} are true. But those are a subset of {(There is something in CO)}. Therefore, we know that none of {3CO or 7CO or 9CO} are true. 13. Since {(There is something in FL)} we know 1 of {5FL} are true. But those are a subset of {(There is a 5 in box 4)}. Therefore, we know that none of {5DJ or 5EK or 5EL or 5FJ or 5FK} are true. 14. Since {(There is something in FL)} we know 1 of {5FL} are true. But those are a subset of {(There is a 5 in column L)}. Therefore, we know that none of {5BL or 5EL or 5IL} are true. 15. Since {(There is something in FL)} we know 1 of {5FL} are true. But those are a subset of {(There is a 5 in row F)}. Therefore, we know that none of {5FJ or 5FK} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 3 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | 7 | | 7 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | 7 | 7 9 | 7 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 3 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 | | | 5 | 4 | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | 9 | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | 3 | 3 | 3 | | 3 | 2 | E | | 4 6 | 6 | 5 | 4 | | 4 5 | 5 | | | 8 | 9 | 9 | 9 | | 9 | 7 | 7 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | 4 | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in CO) will enslave (There is a 4 in row C) (There is something in CO) will enslave (There is a 4 in column O) (There is something in FL) will enslave (There is a 5 in row F) (There is something in FL) will enslave (There is a 5 in column L) (There is something in FL) will enslave (There is a 5 in box 4) (There is something in FR) will enslave (There is a 8 in row F) (There is something in FR) will enslave (There is a 8 in column R) (There is a 1 in row D) will enslave (There is a 1 in box 5) (There is a 6 in row D) will enslave (There is a 6 in box 6) (There is a 1 in row E) will enslave (There is a 1 in box 4) (There is a 6 in row E) will enslave (There is a 6 in box 4) (There is a 7 in row E) will enslave (There is a 7 in box 6) (There is a 7 in row F) will enslave (There is a 7 in box 5) (There is a 4 in column N) will enslave (There is a 4 in box 5) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 3 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | 7 | | 7 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | 7 | 7 9 | 7 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 3 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 | | | 5 | 4 | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | 9 | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | 3 | 3 | 3 | | 3 | 2 | E | | 4 6 | 6 | 5 | 4 | | 4 5 | 5 | | | 8 | 9 | 9 | 9 | | 9 | 7 | 7 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | 4 | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 6 Deductions found: 1. Since {(There is a 3 in box 6)} we know 1 of {3EQ} are true. But those are a subset of {(There is a 3 in column Q)}. Therefore, we know that none of {3AQ or 3CQ} are true. 2. Since {(There is a 3 in box 6)} we know 1 of {3EQ} are true. But those are a subset of {(There is a 3 in row E)}. Therefore, we know that none of {3EM or 3EN or 3EO} are true. 3. Since {(There is a 3 in box 6)} we know 1 of {3EQ} are true. But those are a subset of {(There is something in EQ)}. Therefore, we know that none of {5EQ or 7EQ} are true. 4. Since {(There is a 3 in column R)} we know 1 of {3BR or 3CR} are true. But those are a subset of {(There is a 3 in box 3)}. Therefore, we know that none of {3AQ or 3CQ} are true. 5. Since {(There is a 7 in column M)} we know 1 of {7AM or 7CM} are true. But those are a subset of {(There is a 7 in box 2)}. Therefore, we know that none of {7AN or 7BN or 7BO} are true. 6. Since {(There is a 3 in row F)} we know 1 of {3FN or 3FO} are true. But those are a subset of {(There is a 3 in box 5)}. Therefore, we know that none of {3EM or 3EN or 3EO} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | | | 7 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | | 9 | 7 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 | | | 5 | 4 | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | 9 | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 4 6 | 6 | 5 | 4 | | 4 5 | | | | 8 | 9 | 9 | 9 | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | 4 | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in EQ) will enslave (There is a 3 in row E) (There is something in EQ) will enslave (There is a 3 in column Q) (There is something in EQ) will enslave (There is a 3 in box 6) (There is a 3 in row F) will enslave (There is a 3 in box 5) (There is a 7 in column M) will enslave (There is a 7 in box 2) (There is a 3 in column R) will enslave (There is a 3 in box 3) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | | | 7 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | | 9 | 7 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 | | | 5 | 4 | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | 9 | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 4 6 | 6 | 5 | 4 | | 4 5 | | | | 8 | 9 | 9 | 9 | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | 4 | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 8 Deductions found: 1. Since {(There is a 7 in column Q)} we know 1 of {7AQ or 7CQ} are true. But those are a subset of {(There is a 7 in box 3)}. Therefore, we know that none of {7AP or 7BP} are true. 2. Since {(There is a 7 in row E)} we know 1 of {7EP} are true. But those are a subset of {(There is a 7 in column P)}. Therefore, we know that none of {7AP or 7BP} are true. 3. Since {(There is a 7 in row E)} we know 1 of {7EP} are true. But those are a subset of {(There is something in EP)}. Therefore, we know that none of {4EP or 5EP} are true. 4. Since {(There is something in EO)} we know 1 of {9EO} are true. But those are a subset of {(There is a 9 in box 5)}. Therefore, we know that none of {9DM or 9EM} are true. 5. Since {(There is something in EO)} we know 1 of {9EO} are true. But those are a subset of {(There is a 9 in column O)}. Therefore, we know that none of {9BO} are true. 6. Since {(There is something in EO)} we know 1 of {9EO} are true. But those are a subset of {(There is a 9 in row E)}. Therefore, we know that none of {9EK or 9EL or 9EM} are true. 7. Since {(There is something in EN)} we know 1 of {4EN} are true. But those are a subset of {(There is a 4 in column N)}. Therefore, we know that none of {4DN or 4FN} are true. 8. Since {(There is something in EN)} we know 1 of {4EN} are true. But those are a subset of {(There is a 4 in row E)}. Therefore, we know that none of {4EK or 4EP} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | | | 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 | | | 5 | | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in EM) will enslave (There is a 5 in row E) (There is something in EN) will enslave (There is a 4 in row E) (There is something in EN) will enslave (There is a 4 in column N) (There is something in EO) will enslave (There is a 9 in row E) (There is something in EO) will enslave (There is a 9 in column O) (There is something in EO) will enslave (There is a 9 in box 5) (There is something in EP) will enslave (There is a 7 in row E) (There is something in EP) will enslave (There is a 7 in column P) (There is a 9 in row D) will enslave (There is a 9 in box 4) (There is a 9 in column M) will enslave (There is a 9 in box 2) (There is a 7 in column Q) will enslave (There is a 7 in box 3) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | 7 9 | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 3 | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | 5 | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 9 | 9 | 9 | 8 | | | 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 3 | | 1 2 | 1 2 | | | | | D | 4 | | | 5 | | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | 9 | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 8 Deductions found: 1. Since {(There is a 5 in box 6)} we know 1 of {5DP or 5DQ} are true. But those are a subset of {(There is a 5 in row D)}. Therefore, we know that none of {5DM} are true. 2. Since {(There is a 4 in box 6)} we know 1 of {4DP or 4DR} are true. But those are a subset of {(There is a 4 in row D)}. Therefore, we know that none of {4DJ} are true. 3. Since {(There is a 4 in row F)} we know 1 of {4FJ or 4FK} are true. But those are a subset of {(There is a 4 in box 4)}. Therefore, we know that none of {4DJ} are true. 4. Since {(There is a 9 in row D)} we know 1 of {9DJ} are true. But those are a subset of {(There is a 9 in column J)}. Therefore, we know that none of {9AJ or 9BJ or 9HJ} are true. 5. Since {(There is a 9 in row D)} we know 1 of {9DJ} are true. But those are a subset of {(There is something in DJ)}. Therefore, we know that none of {2DJ or 4DJ} are true. 6. Since {(There is a 7 in row B)} we know 1 of {7BJ} are true. But those are a subset of {(There is a 7 in column J)}. Therefore, we know that none of {7AJ} are true. 7. Since {(There is a 7 in row B)} we know 1 of {7BJ} are true. But those are a subset of {(There is something in BJ)}. Therefore, we know that none of {2BJ or 3BJ or 5BJ or 9BJ} are true. 8. Since {(There is something in EM)} we know 1 of {5EM} are true. But those are a subset of {(There is a 5 in column M)}. Therefore, we know that none of {5DM} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 | 9 | 9 | 8 | | | 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 2 | | | | | D | | | | | | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in BJ) will enslave (There is a 7 in row B) (There is something in BJ) will enslave (There is a 7 in column J) (There is something in DJ) will enslave (There is a 9 in row D) (There is something in DJ) will enslave (There is a 9 in column J) (There is something in EM) will enslave (There is a 5 in column M) (There is a 4 in row D) will enslave (There is a 4 in box 6) (There is a 5 in row D) will enslave (There is a 5 in box 6) (There is a 4 in row F) will enslave (There is a 4 in box 4) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 3 | 1 3 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 2 | 3 | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 6 | 6 | | 6 | 6 | | 4 | | | 7 | 9 | 9 | 8 | | | 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | 3 | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 2 | | | | | D | | | | | | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | 2 | | | 2 3 | 3 | 1 | | | F | 4 | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 4 5 | 4 5 | | | | 6 | 4 5 | 5 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | 5 | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 14 Deductions found: 1. Since {(There is a 2 in box 4)} we know 1 of {2FJ or 2FK} are true. But those are a subset of {(There is a 2 in row F)}. Therefore, we know that none of {2FN} are true. 2. Since {(There is a 2 in box 1)} we know 1 of {2BK or 2CK} are true. But those are a subset of {(There is a 2 in column K)}. Therefore, we know that none of {2FK} are true. 3. Since {(There is a 5 in column J)} we know 1 of {5GJ} are true. But those are a subset of {(There is a 5 in box 7)}. Therefore, we know that none of {5GK or 5IK} are true. 4. Since {(There is a 5 in column J)} we know 1 of {5GJ} are true. But those are a subset of {(There is a 5 in row G)}. Therefore, we know that none of {5GK or 5GP or 5GQ} are true. 5. Since {(There is a 5 in column J)} we know 1 of {5GJ} are true. But those are a subset of {(There is something in GJ)}. Therefore, we know that none of {3GJ or 4GJ} are true. 6. Since {(There is a 2 in column J)} we know 1 of {2FJ} are true. But those are a subset of {(There is a 2 in box 4)}. Therefore, we know that none of {2FK} are true. 7. Since {(There is a 2 in column J)} we know 1 of {2FJ} are true. But those are a subset of {(There is a 2 in row F)}. Therefore, we know that none of {2FK or 2FN} are true. 8. Since {(There is a 2 in column J)} we know 1 of {2FJ} are true. But those are a subset of {(There is something in FJ)}. Therefore, we know that none of {4FJ} are true. 9. Since {(There is a 2 in row D)} we know 1 of {2DM or 2DN} are true. But those are a subset of {(There is a 2 in box 5)}. Therefore, we know that none of {2FN} are true. 10. Since {(There is a 5 in row B)} we know 1 of {5BK} are true. But those are a subset of {(There is a 5 in column K)}. Therefore, we know that none of {5GK or 5IK} are true. 11. Since {(There is a 5 in row B)} we know 1 of {5BK} are true. But those are a subset of {(There is something in BK)}. Therefore, we know that none of {2BK or 6BK or 9BK} are true. 12. Since {(There is something in AJ)} we know 1 of {3AJ} are true. But those are a subset of {(There is a 3 in box 1)}. Therefore, we know that none of {3BL or 3CL} are true. 13. Since {(There is something in AJ)} we know 1 of {3AJ} are true. But those are a subset of {(There is a 3 in column J)}. Therefore, we know that none of {3GJ or 3HJ} are true. 14. Since {(There is something in AJ)} we know 1 of {3AJ} are true. But those are a subset of {(There is a 3 in row A)}. Therefore, we know that none of {3AM or 3AN} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 | 1 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 | 6 | | 6 | 6 | | 4 | | | 7 | | 9 | 8 | | | 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 2 | | | | | D | | | | | | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | 3 | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 5 | 4 | | | | 6 | 4 | 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in AJ) will enslave (There is a 3 in row A) (There is something in AJ) will enslave (There is a 3 in column J) (There is something in AJ) will enslave (There is a 3 in box 1) (There is something in BK) will enslave (There is a 5 in row B) (There is something in BK) will enslave (There is a 5 in column K) (There is something in FJ) will enslave (There is a 2 in row F) (There is something in FJ) will enslave (There is a 2 in column J) (There is something in FJ) will enslave (There is a 2 in box 4) (There is something in FK) will enslave (There is a 4 in row F) (There is something in GJ) will enslave (There is a 5 in row G) (There is something in GJ) will enslave (There is a 5 in column J) (There is something in GJ) will enslave (There is a 5 in box 7) (There is something in HJ) will enslave (There is a 4 in column J) (There is a 2 in row D) will enslave (There is a 2 in box 5) (There is a 5 in row I) will enslave (There is a 5 in box 9) (There is a 2 in column K) will enslave (There is a 2 in box 1) (There is a 3 in column L) will enslave (There is a 3 in box 7) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 | 1 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 | 6 | | 6 | 6 | | 4 | | | 7 | | 9 | 8 | | | 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | 2 | 3 | C | | | | | 5 | 4 | 6 | | | | | 8 9 | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 2 | | | | | D | | | | | | | 4 5 | 5 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | 3 | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 5 | 4 | | | | 6 | 4 | 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 1 3 | 1 2 3 | 1 2 3 | | 2 | 1 2 | 1 | H | 4 | | | | 6 | 5 | 4 | 6 | 4 6 | | | 7 | 8 9 | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | 1 2 | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 15 Deductions found: 1. Since {(There is a 5 in column P)} we know 1 of {5DP} are true. But those are a subset of {(There is a 5 in row D)}. Therefore, we know that none of {5DQ} are true. 2. Since {(There is a 5 in column P)} we know 1 of {5DP} are true. But those are a subset of {(There is something in DP)}. Therefore, we know that none of {4DP} are true. 3. Since {(There is a 3 in column L)} we know 1 of {3HL} are true. But those are a subset of {(There is a 3 in row H)}. Therefore, we know that none of {3HM or 3HN} are true. 4. Since {(There is a 3 in column L)} we know 1 of {3HL} are true. But those are a subset of {(There is something in HL)}. Therefore, we know that none of {1HL or 8HL or 9HL} are true. 5. Since {(There is a 2 in column K)} we know 1 of {2CK} are true. But those are a subset of {(There is a 2 in row C)}. Therefore, we know that none of {2CQ} are true. 6. Since {(There is a 2 in column K)} we know 1 of {2CK} are true. But those are a subset of {(There is something in CK)}. Therefore, we know that none of {8CK or 9CK} are true. 7. Since {(There is a 5 in row I)} we know 1 of {5IQ} are true. But those are a subset of {(There is a 5 in column Q)}. Therefore, we know that none of {5DQ} are true. 8. Since {(There is a 5 in row I)} we know 1 of {5IQ} are true. But those are a subset of {(There is something in IQ)}. Therefore, we know that none of {1IQ or 2IQ or 8IQ} are true. 9. Since {(There is a 3 in row G)} we know 1 of {3GM or 3GO} are true. But those are a subset of {(There is a 3 in box 8)}. Therefore, we know that none of {3HM or 3HN} are true. 10. Since {(There is a 2 in row B)} we know 1 of {2BP} are true. But those are a subset of {(There is a 2 in box 3)}. Therefore, we know that none of {2CQ} are true. 11. Since {(There is a 2 in row B)} we know 1 of {2BP} are true. But those are a subset of {(There is a 2 in column P)}. Therefore, we know that none of {2HP} are true. 12. Since {(There is a 2 in row B)} we know 1 of {2BP} are true. But those are a subset of {(There is something in BP)}. Therefore, we know that none of {9BP} are true. 13. Since {(There is something in HJ)} we know 1 of {4HJ} are true. But those are a subset of {(There is a 4 in box 7)}. Therefore, we know that none of {4GK} are true. 14. Since {(There is something in HJ)} we know 1 of {4HJ} are true. But those are a subset of {(There is a 4 in row H)}. Therefore, we know that none of {4HP or 4HR} are true. 15. Since {(There is something in FK)} we know 1 of {4FK} are true. But those are a subset of {(There is a 4 in column K)}. Therefore, we know that none of {4GK} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 | 1 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 | 6 | | 6 | 6 | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 2 | | | | | D | | | | | | | 5 | 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | 3 | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 5 | | | | | 6 | 4 | 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 2 | 1 2 | | | 1 2 | 1 | H | 4 | | | | 6 | 5 | | 6 | 6 | | | 7 | | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in BP) will enslave (There is a 2 in row B) (There is something in BP) will enslave (There is a 2 in column P) (There is something in BP) will enslave (There is a 2 in box 3) (There is something in CK) will enslave (There is a 2 in row C) (There is something in CK) will enslave (There is a 2 in column K) (There is something in DP) will enslave (There is a 5 in row D) (There is something in DP) will enslave (There is a 5 in column P) (There is something in FK) will enslave (There is a 4 in column K) (There is something in HJ) will enslave (There is a 4 in row H) (There is something in HJ) will enslave (There is a 4 in box 7) (There is something in HL) will enslave (There is a 3 in row H) (There is something in HL) will enslave (There is a 3 in column L) (There is something in IQ) will enslave (There is a 5 in row I) (There is something in IQ) will enslave (There is a 5 in column Q) (There is a 4 in row D) will enslave (There is a 4 in column R) (There is a 3 in row G) will enslave (There is a 3 in box 8) (There is a 4 in row G) will enslave (There is a 4 in column P) (There is a 4 in row G) will enslave (There is a 4 in box 9) (There is a 2 in column Q) will enslave (There is a 2 in box 9) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 | 1 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 | 6 | | 6 | 6 | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 2 | | | | | D | | | | | | | 5 | 6 | 4 6 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | 3 | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 5 | | | | | 6 | 4 | 6 | | | | 8 | | | 9 | | 8 | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 2 | 1 2 | | | 1 2 | 1 | H | 4 | | | | 6 | 5 | | 6 | 6 | | | 7 | | | 8 | | 8 9 | 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 1 2 | 1 | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | 7 8 | 7 | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 11 Deductions found: 1. Since {(There is a 9 in box 7)} we know 1 of {9IK or 9IL} are true. But those are a subset of {(There is a 9 in row I)}. Therefore, we know that none of {9IR} are true. 2. Since {(There is a 2 in column Q)} we know 1 of {2HQ} are true. But those are a subset of {(There is a 2 in row H)}. Therefore, we know that none of {2HM or 2HN} are true. 3. Since {(There is a 2 in column Q)} we know 1 of {2HQ} are true. But those are a subset of {(There is something in HQ)}. Therefore, we know that none of {1HQ or 6HQ or 8HQ} are true. 4. Since {(There is a 2 in row I)} we know 1 of {2IN} are true. But those are a subset of {(There is a 2 in box 8)}. Therefore, we know that none of {2HM or 2HN} are true. 5. Since {(There is a 2 in row I)} we know 1 of {2IN} are true. But those are a subset of {(There is a 2 in column N)}. Therefore, we know that none of {2DN or 2HN} are true. 6. Since {(There is a 2 in row I)} we know 1 of {2IN} are true. But those are a subset of {(There is something in IN)}. Therefore, we know that none of {1IN or 7IN or 8IN} are true. 7. Since {(There is a 9 in row H)} we know 1 of {9HP or 9HR} are true. But those are a subset of {(There is a 9 in box 9)}. Therefore, we know that none of {9IR} are true. 8. Since {(There is a 4 in row G)} we know 1 of {4GP} are true. But those are a subset of {(There is something in GP)}. Therefore, we know that none of {8GP} are true. 9. Since {(There is a 4 in row D)} we know 1 of {4DR} are true. But those are a subset of {(There is something in DR)}. Therefore, we know that none of {6DR} are true. 10. Since {(There is something in DQ)} we know 1 of {6DQ} are true. But those are a subset of {(There is a 6 in column Q)}. Therefore, we know that none of {6GQ or 6HQ} are true. 11. Since {(There is something in DQ)} we know 1 of {6DQ} are true. But those are a subset of {(There is a 6 in row D)}. Therefore, we know that none of {6DR} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 | 1 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 | 6 | | 6 | 6 | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | 3 | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 5 | | | | | 6 | 4 | | | | | 8 | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | 1 | | | 2 | 1 | H | 4 | | | | 6 | 5 | | | 6 | | | 7 | | | 8 | | 8 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 2 | 1 | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in DQ) will enslave (There is a 6 in row D) (There is something in DQ) will enslave (There is a 6 in column Q) (There is something in DR) will enslave (There is a 4 in row D) (There is something in GP) will enslave (There is a 4 in row G) (There is something in HQ) will enslave (There is a 2 in row H) (There is something in HQ) will enslave (There is a 2 in column Q) (There is something in IN) will enslave (There is a 2 in row I) (There is something in IN) will enslave (There is a 2 in column N) (There is something in IN) will enslave (There is a 2 in box 8) (There is a 2 in row D) will enslave (There is a 2 in column M) (There is a 9 in row H) will enslave (There is a 9 in box 9) (There is a 9 in row I) will enslave (There is a 9 in box 7) (There is a 6 in column R) will enslave (There is a 6 in box 9) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | 1 | 1 | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 1 3 | 1 3 | 2 | | 1 3 | B | | 5 | 6 | | 6 | 6 | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 1 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | 3 | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | 7 | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 1 3 | | 1 3 | | 1 | | G | 5 | | | | | 6 | 4 | | | | | 8 | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | 1 | | | 2 | 1 | H | 4 | | | | 6 | 5 | | | 6 | | | 7 | | | 8 | | 8 9 | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | 2 | 1 | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 21 Deductions found: 1. Since {(There is a 6 in column R)} we know 1 of {6HR} are true. But those are a subset of {(There is a 6 in row H)}. Therefore, we know that none of {6HN} are true. 2. Since {(There is a 6 in column R)} we know 1 of {6HR} are true. But those are a subset of {(There is something in HR)}. Therefore, we know that none of {1HR or 9HR} are true. 3. Since {(There is a 8 in column N)} we know 1 of {8HN} are true. But those are a subset of {(There is a 8 in row H)}. Therefore, we know that none of {8HP} are true. 4. Since {(There is a 8 in column N)} we know 1 of {8HN} are true. But those are a subset of {(There is something in HN)}. Therefore, we know that none of {1HN or 6HN} are true. 5. Since {(There is a 7 in column N)} we know 1 of {7FN} are true. But those are a subset of {(There is a 7 in row F)}. Therefore, we know that none of {7FO} are true. 6. Since {(There is a 7 in column N)} we know 1 of {7FN} are true. But those are a subset of {(There is something in FN)}. Therefore, we know that none of {3FN} are true. 7. Since {(There is a 8 in row I)} we know 1 of {8IK or 8IL} are true. But those are a subset of {(There is a 8 in box 7)}. Therefore, we know that none of {8GK} are true. 8. Since {(There is a 7 in row I)} we know 1 of {7IO} are true. But those are a subset of {(There is a 7 in column O)}. Therefore, we know that none of {7FO} are true. 9. Since {(There is a 7 in row I)} we know 1 of {7IO} are true. But those are a subset of {(There is something in IO)}. Therefore, we know that none of {1IO} are true. 10. Since {(There is a 6 in row G)} we know 1 of {6GO} are true. But those are a subset of {(There is a 6 in box 8)}. Therefore, we know that none of {6HN} are true. 11. Since {(There is a 6 in row G)} we know 1 of {6GO} are true. But those are a subset of {(There is a 6 in column O)}. Therefore, we know that none of {6BO} are true. 12. Since {(There is a 6 in row G)} we know 1 of {6GO} are true. But those are a subset of {(There is something in GO)}. Therefore, we know that none of {1GO or 3GO} are true. 13. Since {(There is a 2 in row D)} we know 1 of {2DM} are true. But those are a subset of {(There is something in DM)}. Therefore, we know that none of {1DM} are true. 14. Since {(There is something in IR)} we know 1 of {1IR} are true. But those are a subset of {(There is a 1 in box 9)}. Therefore, we know that none of {1GQ or 1HR} are true. 15. Since {(There is something in IR)} we know 1 of {1IR} are true. But those are a subset of {(There is a 1 in column R)}. Therefore, we know that none of {1BR or 1HR} are true. 16. Since {(There is something in IR)} we know 1 of {1IR} are true. But those are a subset of {(There is a 1 in row I)}. Therefore, we know that none of {1IK or 1IL or 1IO} are true. 17. Since {(There is something in HM)} we know 1 of {1HM} are true. But those are a subset of {(There is a 1 in box 8)}. Therefore, we know that none of {1GM or 1GO or 1HN or 1IO} are true. 18. Since {(There is something in HM)} we know 1 of {1HM} are true. But those are a subset of {(There is a 1 in column M)}. Therefore, we know that none of {1AM or 1DM or 1GM} are true. 19. Since {(There is something in HM)} we know 1 of {1HM} are true. But those are a subset of {(There is a 1 in row H)}. Therefore, we know that none of {1HN or 1HR} are true. 20. Since {(There is something in DN)} we know 1 of {1DN} are true. But those are a subset of {(There is a 1 in column N)}. Therefore, we know that none of {1AN or 1BN or 1HN} are true. 21. Since {(There is something in DN)} we know 1 of {1DN} are true. But those are a subset of {(There is a 1 in row D)}. Therefore, we know that none of {1DM} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | | | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 3 | 1 3 | 2 | | 3 | B | | 5 | 6 | | 6 | | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 3 | | | | | | G | 5 | | | | | 6 | 4 | | | | | | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | | | | 2 | | H | 4 | | | | | 5 | | | 6 | | | 7 | | | 8 | | 9 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 2 | | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in DM) will enslave (There is a 2 in row D) (There is something in DN) will enslave (There is a 1 in row D) (There is something in DN) will enslave (There is a 1 in column N) (There is something in FN) will enslave (There is a 7 in row F) (There is something in FN) will enslave (There is a 7 in column N) (There is something in FO) will enslave (There is a 3 in row F) (There is something in GK) will enslave (There is a 1 in row G) (There is something in GK) will enslave (There is a 1 in box 7) (There is something in GM) will enslave (There is a 3 in row G) (There is something in GO) will enslave (There is a 6 in row G) (There is something in GO) will enslave (There is a 6 in column O) (There is something in GO) will enslave (There is a 6 in box 8) (There is something in GQ) will enslave (There is a 8 in row G) (There is something in GQ) will enslave (There is a 8 in box 9) (There is something in HM) will enslave (There is a 1 in row H) (There is something in HM) will enslave (There is a 1 in column M) (There is something in HM) will enslave (There is a 1 in box 8) (There is something in HN) will enslave (There is a 8 in row H) (There is something in HN) will enslave (There is a 8 in column N) (There is something in HP) will enslave (There is a 9 in row H) (There is something in HR) will enslave (There is a 6 in row H) (There is something in HR) will enslave (There is a 6 in column R) (There is something in IO) will enslave (There is a 7 in row I) (There is something in IO) will enslave (There is a 7 in column O) (There is something in IR) will enslave (There is a 1 in row I) (There is something in IR) will enslave (There is a 1 in column R) (There is something in IR) will enslave (There is a 1 in box 9) (There is a 1 in row A) will enslave (There is a 1 in column Q) (There is a 1 in row A) will enslave (There is a 1 in box 3) (There is a 1 in row B) will enslave (There is a 1 in column O) (There is a 1 in row B) will enslave (There is a 1 in box 2) (There is a 8 in row I) will enslave (There is a 8 in box 7) (There is a 6 in column N) will enslave (There is a 6 in box 2) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | | | 2 | | 1 | | A | | 6 | 4 | | 6 | | | | 5 | | | 8 9 | | 7 9 | | | 8 9 | 7 8 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 3 | 1 3 | 2 | | 3 | B | | 5 | 6 | | 6 | | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | 3 | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 8 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 1 | | | | | 3 | 2 | E | | 6 | 6 | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 3 | | | | | | G | 5 | | | | | 6 | 4 | | | | | | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | | | | 2 | | H | 4 | | | | | 5 | | | 6 | | | 7 | | | 8 | | 9 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 2 | | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 18 Deductions found: 1. Since {(There is a 9 in column R)} we know 1 of {9BR or 9CR} are true. But those are a subset of {(There is a 9 in box 3)}. Therefore, we know that none of {9AP} are true. 2. Since {(There is a 8 in column P)} we know 1 of {8AP} are true. But those are a subset of {(There is a 8 in box 3)}. Therefore, we know that none of {8AQ or 8CQ} are true. 3. Since {(There is a 8 in column P)} we know 1 of {8AP} are true. But those are a subset of {(There is a 8 in row A)}. Therefore, we know that none of {8AK or 8AQ} are true. 4. Since {(There is a 8 in column P)} we know 1 of {8AP} are true. But those are a subset of {(There is something in AP)}. Therefore, we know that none of {9AP} are true. 5. Since {(There is a 3 in column N)} we know 1 of {3BN} are true. But those are a subset of {(There is a 3 in box 2)}. Therefore, we know that none of {3BO or 3CM} are true. 6. Since {(There is a 3 in column N)} we know 1 of {3BN} are true. But those are a subset of {(There is a 3 in row B)}. Therefore, we know that none of {3BO or 3BR} are true. 7. Since {(There is a 3 in column N)} we know 1 of {3BN} are true. But those are a subset of {(There is something in BN)}. Therefore, we know that none of {6BN} are true. 8. Since {(There is a 1 in column L)} we know 1 of {1EL} are true. But those are a subset of {(There is a 1 in row E)}. Therefore, we know that none of {1EK} are true. 9. Since {(There is a 1 in column L)} we know 1 of {1EL} are true. But those are a subset of {(There is something in EL)}. Therefore, we know that none of {6EL} are true. 10. Since {(There is a 1 in row B)} we know 1 of {1BO} are true. But those are a subset of {(There is something in BO)}. Therefore, we know that none of {3BO} are true. 11. Since {(There is a 1 in row A)} we know 1 of {1AQ} are true. But those are a subset of {(There is something in AQ)}. Therefore, we know that none of {7AQ or 8AQ} are true. 12. Since {(There is something in HP)} we know 1 of {9HP} are true. But those are a subset of {(There is a 9 in column P)}. Therefore, we know that none of {9AP} are true. 13. Since {(There is something in GQ)} we know 1 of {8GQ} are true. But those are a subset of {(There is a 8 in column Q)}. Therefore, we know that none of {8AQ or 8CQ} are true. 14. Since {(There is something in GM)} we know 1 of {3GM} are true. But those are a subset of {(There is a 3 in column M)}. Therefore, we know that none of {3CM} are true. 15. Since {(There is something in GK)} we know 1 of {1GK} are true. But those are a subset of {(There is a 1 in column K)}. Therefore, we know that none of {1EK} are true. 16. Since {(There is something in FO)} we know 1 of {3FO} are true. But those are a subset of {(There is a 3 in column O)}. Therefore, we know that none of {3BO} are true. 17. Since {(There is something in AN)} we know 1 of {6AN} are true. But those are a subset of {(There is a 6 in column N)}. Therefore, we know that none of {6BN} are true. 18. Since {(There is something in AN)} we know 1 of {6AN} are true. But those are a subset of {(There is a 6 in row A)}. Therefore, we know that none of {6AK} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | | | 2 | | 1 | | A | | | 4 | | 6 | | | | 5 | | | 9 | | 7 9 | | | 8 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 3 | 1 | 2 | | | B | | 5 | 6 | | | | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 1 | | | | | 3 | 2 | E | | 6 | | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 3 | | | | | | G | 5 | | | | | 6 | 4 | | | | | | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | | | | 2 | | H | 4 | | | | | 5 | | | 6 | | | 7 | | | 8 | | 9 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 2 | | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in AN) will enslave (There is a 6 in row A) (There is something in AN) will enslave (There is a 6 in column N) (There is something in AP) will enslave (There is a 8 in row A) (There is something in AP) will enslave (There is a 8 in column P) (There is something in AP) will enslave (There is a 8 in box 3) (There is something in AQ) will enslave (There is a 1 in row A) (There is something in BN) will enslave (There is a 3 in row B) (There is something in BN) will enslave (There is a 3 in column N) (There is something in BN) will enslave (There is a 3 in box 2) (There is something in BO) will enslave (There is a 1 in row B) (There is something in CQ) will enslave (There is a 7 in column Q) (There is something in EK) will enslave (There is a 6 in row E) (There is something in EK) will enslave (There is a 6 in column K) (There is something in EL) will enslave (There is a 1 in row E) (There is something in EL) will enslave (There is a 1 in column L) (There is something in FO) will enslave (There is a 3 in column O) (There is something in GK) will enslave (There is a 1 in column K) (There is something in GM) will enslave (There is a 3 in column M) (There is something in GQ) will enslave (There is a 8 in column Q) (There is something in HP) will enslave (There is a 9 in column P) (There is a 6 in row B) will enslave (There is a 6 in column L) (There is a 6 in row B) will enslave (There is a 6 in box 1) (There is a 3 in row C) will enslave (There is a 3 in column R) (There is a 8 in row C) will enslave (There is a 8 in box 1) (There is a 9 in column R) will enslave (There is a 9 in box 3) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | | | 2 | | 1 | | A | | | 4 | | 6 | | | | 5 | | | 9 | | 7 9 | | | 8 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 3 | 1 | 2 | | | B | | 5 | 6 | | | | | 4 | | | 7 | | 9 | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 9 | 7 9 | | | | 7 | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 1 | | | | | 3 | 2 | E | | 6 | | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 3 | | | | | | G | 5 | | | | | 6 | 4 | | | | | | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | | | | 2 | | H | 4 | | | | | 5 | | | 6 | | | 7 | | | 8 | | 9 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 2 | | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 9 | 8 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 14 Deductions found: 1. Since {(There is a 8 in column K)} we know 1 of {8IK} are true. But those are a subset of {(There is a 8 in row I)}. Therefore, we know that none of {8IL} are true. 2. Since {(There is a 8 in column K)} we know 1 of {8IK} are true. But those are a subset of {(There is something in IK)}. Therefore, we know that none of {9IK} are true. 3. Since {(There is a 8 in row C)} we know 1 of {8CL} are true. But those are a subset of {(There is a 8 in column L)}. Therefore, we know that none of {8IL} are true. 4. Since {(There is a 8 in row C)} we know 1 of {8CL} are true. But those are a subset of {(There is something in CL)}. Therefore, we know that none of {9CL} are true. 5. Since {(There is a 3 in row C)} we know 1 of {3CR} are true. But those are a subset of {(There is something in CR)}. Therefore, we know that none of {9CR} are true. 6. Since {(There is a 6 in row B)} we know 1 of {6BL} are true. But those are a subset of {(There is something in BL)}. Therefore, we know that none of {9BL} are true. 7. Since {(There is a 7 in row A)} we know 1 of {7AM} are true. But those are a subset of {(There is a 7 in column M)}. Therefore, we know that none of {7CM} are true. 8. Since {(There is a 7 in row A)} we know 1 of {7AM} are true. But those are a subset of {(There is something in AM)}. Therefore, we know that none of {9AM} are true. 9. Since {(There is something in CQ)} we know 1 of {7CQ} are true. But those are a subset of {(There is a 7 in row C)}. Therefore, we know that none of {7CM} are true. 10. Since {(There is something in BR)} we know 1 of {9BR} are true. But those are a subset of {(There is a 9 in column R)}. Therefore, we know that none of {9CR} are true. 11. Since {(There is something in BR)} we know 1 of {9BR} are true. But those are a subset of {(There is a 9 in row B)}. Therefore, we know that none of {9BL} are true. 12. Since {(There is something in AK)} we know 1 of {9AK} are true. But those are a subset of {(There is a 9 in box 1)}. Therefore, we know that none of {9BL or 9CL} are true. 13. Since {(There is something in AK)} we know 1 of {9AK} are true. But those are a subset of {(There is a 9 in column K)}. Therefore, we know that none of {9IK} are true. 14. Since {(There is something in AK)} we know 1 of {9AK} are true. But those are a subset of {(There is a 9 in row A)}. Therefore, we know that none of {9AM} are true. Implementing ALL deductions... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | | | 2 | | 1 | | A | | | 4 | | 6 | | | | 5 | | | 9 | | 7 | | | 8 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 3 | 1 | 2 | | | B | | 5 | 6 | | | | | 4 | | | 7 | | | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 | 9 | | | | 7 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 1 | | | | | 3 | 2 | E | | 6 | | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 3 | | | | | | G | 5 | | | | | 6 | 4 | | | | | | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | | | | 2 | | H | 4 | | | | | 5 | | | 6 | | | 7 | | | 8 | | 9 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 2 | | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 | 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ ...Looking for slaves... (There is something in AK) will enslave (There is a 9 in row A) (There is something in AK) will enslave (There is a 9 in column K) (There is something in AK) will enslave (There is a 9 in box 1) (There is something in AM) will enslave (There is a 7 in row A) (There is something in AM) will enslave (There is a 7 in column M) (There is something in BL) will enslave (There is a 6 in row B) (There is something in BR) will enslave (There is a 9 in row B) (There is something in BR) will enslave (There is a 9 in column R) (There is something in CL) will enslave (There is a 8 in row C) (There is something in CL) will enslave (There is a 8 in column L) (There is something in CM) will enslave (There is a 9 in row C) (There is something in CM) will enslave (There is a 9 in column M) (There is something in CQ) will enslave (There is a 7 in row C) (There is something in CR) will enslave (There is a 3 in row C) (There is something in IK) will enslave (There is a 8 in row I) (There is something in IK) will enslave (There is a 8 in column K) (There is something in IL) will enslave (There is a 9 in row I) (There is something in IL) will enslave (There is a 9 in column L) ...stopped looking for slaves... J K L M N O P Q R +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 3 | | | | | 2 | | 1 | | A | | | 4 | | 6 | | | | 5 | | | 9 | | 7 | | | 8 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 3 | 1 | 2 | | | B | | 5 | 6 | | | | | 4 | | | 7 | | | 8 | | | | | 9 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 1 | 2 | | | | | | | 3 | C | | | | | 5 | 4 | 6 | | | | | | 8 | 9 | | | | 7 | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 3 | | 2 | 1 | | | | | D | | | | | | | 5 | 6 | 4 | | 9 | | 7 | | | 8 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 1 | | | | | 3 | 2 | E | | 6 | | 5 | 4 | | | | | | 8 | | | | | 9 | 7 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | 2 | | | | | 3 | 1 | | | F | | 4 | 5 | 6 | | | | | | | | | | | 7 | | | 9 | 8 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | 1 | 2 | 3 | | | | | | G | 5 | | | | | 6 | 4 | | | | | | | | 9 | | | 8 | 7 | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | 3 | 1 | | | | 2 | | H | 4 | | | | | 5 | | | 6 | | | 7 | | | 8 | | 9 | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | | | | | 2 | | 3 | | 1 | I | 6 | | | 4 | | | | 5 | | | | 8 | 9 | | | 7 | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ 0 Deductions found: No more single-deep deductions can be made.