Garden sides: 55, 62, 117 yards. At 10 shillings a square yard, what's the cost?
A neighbour was offered a triangular piece of ground for a garden, its three sides measuring 55 yards, 62 yards and 117 yards, priced at 10 shillings per square yard. What will the garden cost?
Reveal the answer
Nothing: the triangle doesn't exist. Since 55 + 62 = 117 exactly, the three 'sides' lie flat in a straight line and enclose zero area, so there's nothing to buy. Henry Dudeney set this as puzzle no. 325 in his posthumous 1932 collection, 'Puzzles and Curious Problems.'
— Henry Ernest Dudeney, Puzzles and Curious Problems — 1932, puzzle no. 325 (also no. 283 in the 1968 compilation '536 Puzzles & Curious Problems')
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