Mathematical Recreations And Essays

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35. 34), (72. 6. 5), (61. 16. 77), (32. 74. 48), (3. 45. 19), (28. 68. 66), (37. 86. 39), (10. 8. 57), (46. 80. 36), (22. 65. 75), (7. 17. 51), (85. 23. 78), (52. 20. 27), (49. 56. 81), (55. 38. 24). The triplets in the second part are (56. 39. 25), (57. 40. 26), (1. 5. 42), (2. 6. 43), (3. 7. 44), (1. 29. 6), (2. 30. 7), (3. 31. 8), (1. 9. 20), (2. 10. 21), (3. 11. 22), (1. 14. 36), (2. 15. 37), (3. 16. 38).
Before proceeding to the consideration of other methods I should add that it is also p
...ossible to obtain irregular solutions of cases where n is of any of these three forms. As an instance I give a three-step solution of 33 girls.
A possible arrangement in the first part is (1. 4. 10), (14. 23. 26), (9. 15. 30), (3. 28. 83), (2. 6. 8), (11. 18. 27), (13. 24. 25), (5. 16. 20), (7. 17. 22), (21. 29. 31), (12. 19. 32). The triplets in the second part are (1. 2. 21), (1. 8. 30), (1. 3. 26), (1. 15. 20), (1. 17. 18). I describe this solution as irregular, since all, saye one, of the triads used are different.


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