

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.


0




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 nth triangular number.


REFERENCES

Martin Gardner, Penny Puzzles, in Mathematical Carnival, p. 1226, 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 10hole 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



