Here is a puzzle that will, I think, be found as amusing as instructive.  We are given a ring of eight circles.  Leaving circle 8 blank, we are required to write in the name of a seven-lettered port in the United Kingdom in this manner.  Touch a blank circle with your pencil, then jump over two circles in either direction round the ring, and write down the first letter.  Then touch another vacant circle, jump over two circles, and write down your second letter.  Proceed similarly with the other letters in their proper order until you have completed the word.  Thus, suppose we select “Glasgow,” and proceed as follows:  6—­1, 7—­2, 8—­3, 7—­4, 8—­5, which means that we touch 6, jump over 7 and and write down “G” on 1; then touch 7, jump over 8 and 1, and write down “l” on 2; and so on.  It will be found that after we have written down the first five letters—­“Glasg”—­as above, we cannot go any further.  Either there is something wrong with “Glasgow,” or we have not managed our jumps properly.  Can you get to the bottom of the mystery?

227.—­CENTRAL SOLITAIRE.

[Illustration]

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.