A127500 On the triangular peg solitaire board of side n, the shortest solution to any problem beginning with one peg missing and ending with one peg.

5, 9, 9, 12, 13, 16, 18

Offset

4,1

Comments

Shortest means the minimum number of moves, where a move is one or more jumps by the same peg. The reference calculates a(n) up to n=10 and gives the bounds 19<=a(11)<=28, 21<=a(12)<=29, as well as an upper bound for n a multiple of 12. A trivial upper bound is a(n)<=T(n)-2, where T(n) is the n-th triangular number.

References

Martin Gardner, Penny Puzzles, in Mathematical Carnival, p. 12-26, Alfred A. Knopf, Inc., 1975

Links

Table of n, a(n) for n=4..10.

George I. Bell, Triangular Peg Solitaire.

George I. Bell, Solving Triangular Peg Solitaire [arXiv:math/0703865v4]

G. I. Bell, Solving Triangular Peg Solitaire, JIS 11 (2008) 08.4.8

Example

a(4)=5, the 10-hole triangular board can be solved in 5 moves (and always 8 jumps).

Crossrefs

Cf. A000217, A102422.

Sequence in context: A175363 A073168 A315121 * A057655 A175374 A141124

Adjacent sequences: A127497 A127498 A127499 * A127501 A127502 A127503

Keyword

hard,more,nonn

Author

George Bell (gibell(AT)comcast.net), Mar 31 2007

Status

approved