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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
5, 9, 9, 12, 13, 16, 18 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)