Dividing-the-Plane Puzzles 101stationary. Although the watchmaker took the machine away for careful
examination, he failed to detect the cause of the strange paradox.- THE FOUR HOUSEHOLDERS
Here is a square plot of land with
four houses, four trees, a well (W) in
the center, and hedges planted across
with four gateways (G).
Can you divide the ground so that
each householder shall have an equal
portion ofland, one tree, one gateway,
an equal length of hedge, and free
access to the well without trespass?
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- THE FIVE FENCES
A man owned a large, square,
fenced-in field in which were sixteen
oak trees, as depicted in the illustra-
tion. He wished, for some eccentric
reason, to put up five straight fences,
so that every tree should be in a
separate enclosure.
How did he do it? Just take your
pencil and draw five straight strokes
across the field, so that every tree shall
be fenced off from all the others.- THE FARMER'S SONS
A farmer once had a square piece of ground on which stood twenty-four
trees, exactly as shown in the illustration on the following page. He left