202 Match Puzzles
being so, what is the smallest number of hurdles that he will require for en-
closing ten sheep? Everything depends on the shape of your enclosure. The
only other way of placing the four matches (or hurdles) in A is to form a
diamond-shaped figure, and the more attenuated this diamond becomes the
smaller will be its area, until the sides meet, when there will be no area enclosed
at all.
If you place six matches, as in B, you will have room for two sheep. But if
you place them as in C, you will only have room for one sheep, for seven-
tenths of a sheep will only exist as mutton. And if you place them as in D, you
can still only accommodate two sheep, which is the maximum for six hurdles.
How many hurdles do you require for ten sheep?
- THE TWENTY MATCHES
The illustration shows how twenty matches, divided into two groups of
fourteen and six, may form two enclosures so that one space enclosed is
exactly three times as large as the other. Now divide the twenty matches into
two groups of thirteen and seven, and with them again make two enclosures,
one exactly three times as large as the other.
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[ I] ] J] I
- A MATCH PUZZLE
The sixteen squares of a chessboard are enclosed by sixteen matches. It is
required to place an odd number of matches inside the square so as to en-