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Solitaire Board

 A "Solitaire" board is a round polished board with holes cut in it in a geometrical pattern, and a glass marble in every hole.  Print an enlarged copy of the above on a sheet of paper, number the "holes," and provide yourself with 33 counters, buttons, or beans.  Now place a counter in every hole except the central one, No. 17. Now take off all the counters in a series of jumps, except the last counter, which must be left in that central hole.  You are allowed to jump one counter over the next one to a vacant hole beyond, and the counter jumped over is immediately taken off the board.  Every move must be a jump; consequently you will take off a counter at each move, and thirty-one single jumps will of course remove all the thirty-one counters.  Compound moves are allowed  for so long as one counter continues to jump, the jumps all count as one move. Here is the beginning of an imaginary solution which will serve to make the manner of moving perfectly plain, and show how you should write out his attempts: 5-17, 12-10, 26-12, 24-26 (13-11, 11-25), 9-11 (26-24, 24-10, 10-12), etc., etc.  The jumps contained within brackets count as one move, because they are made with the same counter.  Find the fewest possible moves. No diagonal jumps are permitted; you can only jump in the direction of the lines. See answer

Math Genius