188.—­THE BALL PROBLEM.

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A stonemason was engaged the other day in cutting out a round ball for the purpose of some architectural decoration, when a smart schoolboy came upon the scene.

“Look here,” said the mason, “you seem to be a sharp youngster, can you tell me this?  If I placed this ball on the level ground, how many other balls of the same size could I lay around it (also on the ground) so that every ball should touch this one?”

The boy at once gave the correct answer, and then put this little question to the mason:—­

“If the surface of that ball contained just as many square feet as its volume contained cubic feet, what would be the length of its diameter?”

The stonemason could not give an answer.  Could you have replied correctly to the mason’s and the boy’s questions?

189.—­THE YORKSHIRE ESTATES.

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I was on a visit to one of the large towns of Yorkshire.  While walking to the railway station on the day of my departure a man thrust a hand-bill upon me, and I took this into the railway carriage and read it at my leisure.  It informed me that three Yorkshire neighbouring estates were to be offered for sale.  Each estate was square in shape, and they joined one another at their corners, just as shown in the diagram.  Estate A contains exactly 370 acres, B contains 116 acres, and C 74 acres.

Now, the little triangular bit of land enclosed by the three square estates was not offered for sale, and, for no reason in particular, I became curious as to the area of that piece.  How many acres did it contain?

190.—­FARMER WURZEL’S ESTATE.

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I will now present another land problem.  The demonstration of the answer that I shall give will, I think, be found both interesting and easy of comprehension.

Farmer Wurzel owned the three square fields shown in the annexed plan, containing respectively 18, 20, and 26 acres.  In order to get a ring-fence round his property he bought the four intervening triangular fields.  The puzzle is to discover what was then the whole area of his estate.

191.—­THE CRESCENT PUZZLE.

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Here is an easy geometrical puzzle.  The crescent is formed by two circles, and C is the centre of the larger circle.  The width of the crescent between B and D is 9 inches, and between E and F 5 inches.  What are the diameters of the two circles?

192.—­THE PUZZLE WALL.

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There was a small lake, around which four poor men built their cottages.  Four rich men afterwards built their mansions, as shown in the illustration, and they wished to have the lake to themselves, so they instructed a builder to put up the shortest possible wall that would exclude the cottagers, but give themselves free access to the lake.  How was the wall to be built?