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Search: id:A127500
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| A127500 |
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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. |
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1
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OFFSET
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4,1
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COMMENT
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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.
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REFERENCES
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Martin Gardner, Penny Puzzles, in Mathematical Carnival, p. 12-26, Alfred A. Knopf, Inc., 1975
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LINKS
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George I. Bell, Triangular Peg Solitaire.
George I. Bell, Solving Triangular Peg Solitaire [arXiv:math/0703865v4]
George I. Bell, A table of solutions, with diagrams.
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EXAMPLE
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a(4)=5, the 10-hole triangular board can be solved in 5 moves (and always 8 jumps).
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CROSSREFS
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Cf. A000217, A102422.
Sequence in context: A020846 A105643 A073168 this_sequence A057655 A141124 A046255
Adjacent sequences: A127497 A127498 A127499 this_sequence A127501 A127502 A127503
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KEYWORD
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hard,more,nonn
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AUTHOR
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George Bell (gibell(AT)comcast.net), Mar 31 2007
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