Source: 1. rec.puzzles. 2. Sun-Tsu Suan Ching, c. 400, in The Penguin Book of Curious and Interesting Puzzles, David Wells, 1992, #69
For the first problem, I find Kirk's graphical solutions easiest to understand. Label the triangle as shown. There are then four different starting positions: 1, 2, 4, and 5. | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
Kirk's answer to largest number of remaining pegs: Start with hole 5 empty. | * * * * . * * * * * * * * * * 5 empty | * * * * * * * . * * * . * * * 12 - 5 | * * . * . * * * * * * . * * * 3 - 8 | * * . * * * * * . * * . * . * 14 - 5 | * * * * . * * . . * * . * . * 8 - 3 |
1 1 10 13 7 2 2 6 11 14 4 3 4 9 12 15 5 13Notice that starting in position 5 means you can ONLY end in position 13. The other starting positions allow an ending in the starting hole. Solutions I've had (A-F = 10-15):
Kirk's Solutions:
Start hole 1
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Start hole 2
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Start hole 4
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Start hole 5
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* * . . . . . * * * * . * * * | . . . * . . . * * * * . * * * | . . . * . . . * * * * * . . * | . . . . . . . . * * * * * . * | . . . . . . . . * * * . . * * |
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We consider the traditional notations of a chess board: 5 * * * * * 4 * * * * * 3 * * * * * 2 * * * * * 1 * * * * * a b c d e question 1 The successful sequence in order to put the peg 9 in the position c3,is the following: c3-c5, b3-d1, c5-a3-c1-e3, d4-d2, d1-d3, e3-c3[This can be done with fewer peg changes - KD: c3-c5-a3-c1-e3, d4-d2, b3-d1-d3, e3-c3]
questions 2 and 3 2 pegs only can be touched, for example b3 and c3 in the following sequence: b3-d1 on one hand and c3-c5-a3-c1-e1-c3-e3-c5 on the other hand question 4 2 diagonal jumps (D) are at least necessary as described hereafter: b3-b5, d4-b4, b5-b3, d3-d1, c3-a3, a3-c1 (D),d1-b1,b1-d3 (D)