Math Puzzle . ca - math and logic puzzles
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THE GARDEN WALLS.
A speculative country builder has a circular field, on which he has
erected four cottages, as shown in the illustration. The field is
surrounded by a brick wall, and the owner undertook to put up three
other brick walls, so that the neighbours should not be overlooked by
each other, but the four tenants insist that there shall be no
favouritism, and that each shall have exactly the same length of wall
space for his wall fruit trees. The puzzle is to show how the three
walls may be built so that each tenant shall have the same area of
ground, and precisely the same length of wall.
Of course, each garden must be entirely enclosed by its walls, and it
must be possible to prove that each garden has exactly the same length
of wall. If the puzzle is properly solved no figures are necessary.