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(Moving Counter Problem)
This ancient puzzle was a great favourite with our grandmothers, and
most of us, I imagine, have on occasions come across a "Solitaire"
board--a round polished board with holes cut in it in a geometrical
pattern, and a glass marble in every hole. Sometimes I have noticed one
on a side table in a suburban front parlour, or found one on a shelf in
a country cottage, or had one brought under my notice at a wayside inn.
Sometimes they are of the form shown above, but it is equally common for
the board to have four more holes, at the points indicated by dots. I
select the simpler form.
Though "Solitaire" boards are still sold at the toy shops, it will be
sufficient if the reader will make an enlarged copy of the above on a
sheet of cardboard or paper, number the "holes," and provide himself
with 33 counters, buttons, or beans. Now place a counter in every hole
except the central one, No. 17, and the puzzle is to 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, just as in the game of draughts, and
the counter jumped over is immediately taken off the board. Only
remember 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. But compound moves are allowed (as in
draughts, again), 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 the solver 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. Of course, no diagonal jumps are permitted; you
can only jump in the direction of the lines.

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