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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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%I #12 Sep 07 2015 13:20:52

%S 5,9,9,12,13,16,18

%N 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.

%C 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.

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

%H George I. Bell, <a href="http://home.comcast.net/~gibell/pegsolitaire/">Triangular Peg Solitaire</a>.

%H George I. Bell, <a href="http://arXiv.org/abs/math.CO/0703865">Solving Triangular Peg Solitaire</a> [arXiv:math/0703865v4]

%H G. I. Bell, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Bell/bell2.html">Solving Triangular Peg Solitaire</a>, JIS 11 (2008) 08.4.8

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

%Y Cf. A000217, A102422.

%K hard,more,nonn

%O 4,1

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