To Perform

"In chess, the Chess Knight does most of the capturing of the opponent's men. This Knight has a peculiar move which it is difficult to explain in words. Wherever on the board the Knight happens to be, it can be moved into any square which is removed from it by two squares not in the same direction. For instance, he could not be moved from number 2 (point to board) over to number 4 or 18 -- but he could be moved through 3 to 12 or through 10 to 19. The final square which he alights on cannot be in the same direction as he is moving, but must be on a slant. Thus, supposing you have moved from 19. The next move would be either back to 2 or to 9, 25, 34, 36, 29, 13, or 4."

As you explain these moves, point to each square with your chalk so that audience will understand them. If you can easily erase them, demonstrate by actually drawing lines through each square as you show moves. Otherwise, just point out squares.

"You will note that the first square into which a move is made is immediately above, below or to the right or left of the starting place. For convenience, let us call the starting square A, the next square passed through B, and the square on which the Knight alights C.

"If we start at number 36, that would be square A. 35, 37, 28, or 44 would be square B. Any number diagonally off these four numbers would be square C. Let us assume that we moved to 37 as square B. Then either 30 or 46 would be square C for Knight to alight on.

"The problem I am going to present is to start the Knight from any square on the board and by a continuous series of sixty-four moves to cause the Knight to alight on each square ONCE and on NO square more than ONCE and to END UP AT THE SQUARE STARTED FROM.

"When you appreciate the peculiar move of the Knight and realize that you have sixty-four places to choose from for his start, you can understand the perplexing problem I have to contend with and the many moves I have to consider.

"Now, I shall ask someone to select one of the 64 numbers from which to start the Chess Knight on his journey.

"The gentlemen here says 29. All right. Here is square 29, just about in the center of the board. Figure 4.

Point to number 29 and draw a diagonal line through it from the upper left corner to the lower right corner. Look at the cue number which you have marked on this square for your next move ~ or if using a card, look at that, but don't allow the audience to see you do it.

"Now I can start by moving through 28, 30, 21, or 37. I shall move through 28 and light on 35."

Point to 28 but do not cross through it. Draw a diagonal line through 35. Then look at cue number in this square. It is 50.

"Then through 43 to 50."

Continue this now through the numbers, one after the other, crossing off the square on which the Knight alights each time. Finally, you will have crossed off number 44, the one before 29.

"And finally, the Knight jumps from number 44 up through 36 and back to the STARTING PLACE -- 29. The Knight has alighted on every number once as you see by the cross lines -- and only once -- and now he is back to 29."

Give a slight bow to bring forth applause.

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