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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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0
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OFFSET
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4,1
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COMMENTS
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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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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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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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STATUS
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approved
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