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Hi-Q

A triangular version of Peg Solitaire with 15 holes and 14 pegs. Numbering hole 1 at the apex of the triangle and thereafter from left to right on the next lower row, etc., the following table gives possible ending holes for a single peg removed (Beeler et al. 1972, Item 76). Because of symmetry, only the first five pegs need be considered. Also because of symmetry, removing peg 2 is equivalent to removing peg 3 and flipping the board horizontally.

remove possible ending pegs
1 1, $7=10$, 13
2 2, 6, 11, 14
4 $3=12$, 4, 9, 15
5 13


References

Beeler, M.; Gosper, R. W.; and Schroeppel, R. Item 75 in HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.




© 1996-9 Eric W. Weisstein
1999-05-25