four passed over are standing alone or piled; they count just the same, and you can always carry a cheese in either direction.  There are a great many different ways of doing it in twelve moves, so it makes a good game of “patience” to try to solve it so that the four piles shall be left in different stipulated places.  For example, try to leave the piles at the extreme ends of the row, on Nos. 1, 2, 15 and 16; this is quite easy.  Then try to leave three piles together, on Nos. 13, 14, and 15.  Then again play so that they shall be left on Nos. 3, 5, 12, and 14.

234.—­THE EXCHANGE PUZZLE.

Here is a rather entertaining little puzzle with moving counters.  You only need twelve counters—­six of one colour, marked A, C, E, G, I, and K, and the other six marked B, D, F, H, J, and L. You first place them on the diagram, as shown in the illustration, and the puzzle is to get them into regular alphabetical order, as follows:—­

A   B   C   D
E   F   G   H
I   J   K   L

The moves are made by exchanges of opposite colours standing on the same line.  Thus, G and J may exchange places, or F and A, but you cannot exchange G and C, or F and D, because in one case they are both white and in the other case both black.  Can you bring about the required arrangement in seventeen exchanges?

[Illustration]

It cannot be done in fewer moves.  The puzzle is really much easier than it looks, if properly attacked.

235.—­TORPEDO PRACTICE.

[Illustration]

If a fleet of sixteen men-of-war were lying at anchor and surrounded by the enemy, how many ships might be sunk if every torpedo, projected in a straight line, passed under three vessels and sank the fourth?  In the diagram we have arranged the fleet in square formation, where it will be seen that as many as seven ships may be sunk (those in the top row and first column) by firing the torpedoes indicated by arrows.  Anchoring the fleet as we like, to what extent can we increase this number?  Remember that each successive ship is sunk before another torpedo is launched, and that every torpedo proceeds in a different direction; otherwise, by placing the ships in a straight line, we might sink as many as thirteen!  It is an interesting little study in naval warfare, and eminently practical—­provided the enemy will allow you to arrange his fleet for your convenience and promise to lie still and do nothing!

236.—­THE HAT PUZZLE.

Ten hats were hung on pegs as shown in the illustration—­five silk hats and five felt “bowlers,” alternately silk and felt.  The two pegs at the end of the row were empty.

[Illustration]

The puzzle is to remove two contiguous hats to the vacant pegs, then two other adjoining hats to the pegs now unoccupied, and so on until five pairs have been moved and the hats again hang in an unbroken row, but with all the silk ones together and all the felt hats together.