Now, a simple little question like this that everybody can perfectly understand will puzzle many people to answer in any way.  Let us see whether, without going into any profound mathematical calculations, we can get the answer roughly—­say, within a mile of what is correct!  We will assume that when the wire is all wound up the ball is perfectly solid throughout, and that no allowance has to be made for the axle that passes through it.  With that simplification, I wonder how many readers can state within even a mile of the correct answer the length of that wire.

201.—­HOW TO MAKE CISTERNS.

[Illustration]

Our friend in the illustration has a large sheet of zinc, measuring (before cutting) eight feet by three feet, and he has cut out square pieces (all of the same size) from the four corners and now proposes to fold up the sides, solder the edges, and make a cistern.  But the point that puzzles him is this:  Has he cut out those square pieces of the correct size in order that the cistern may hold the greatest possible quantity of water?  You see, if you cut them very small you get a very shallow cistern; if you cut them large you get a tall and slender one.  It is all a question of finding a way of cutting put these four square pieces exactly the right size.  How are we to avoid making them too small or too large?

202.—­THE CONE PUZZLE.

[Illustration]

I have a wooden cone, as shown in Fig. 1.  How am I to cut out of it the greatest possible cylinder?  It will be seen that I can cut out one that is long and slender, like Fig. 2, or short and thick, like Fig. 3.  But neither is the largest possible.  A child could tell you where to cut, if he knew the rule.  Can you find this simple rule?

203.—­CONCERNING WHEELS.

[Illustration]

There are some curious facts concerning the movements of wheels that are apt to perplex the novice.  For example:  when a railway train is travelling from London to Crewe certain parts of the train at any given moment are actually moving from Crewe towards London.  Can you indicate those parts?  It seems absurd that parts of the same train can at any time travel in opposite directions, but such is the case.

In the accompanying illustration we have two wheels.  The lower one is supposed to be fixed and the upper one running round it in the direction of the arrows.  Now, how many times does the upper wheel turn on its own axis in making a complete revolution of the other wheel?  Do not be in a hurry with your answer, or you are almost certain to be wrong.  Experiment with two pennies on the table and the correct answer will surprise you, when you succeed in seeing it.

204.—­A NEW MATCH PUZZLE.

[Illustration]

In the illustration eighteen matches are shown arranged so that they enclose two spaces, one just twice as large as the other.  Can you rearrange them (1) so as to enclose two four-sided spaces, one exactly three times as large as the other, and (2) so as to enclose two five-sided spaces, one exactly three times as large as the other?  All the eighteen matches must be fairly used in each case; the two spaces must be quite detached, and there must be no loose ends or duplicated matches.