Enigma 1758: Path-o-logical
17 July 2013
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From New Scientist #2926, 20th July 2013 [link]
Our local park is rectangular, with each of its sides a whole number of metres in length, the longer sides exceeding the shorter ones by 25 metres. The boundaries run north-south and east-west. There are two straight paths of equal length. One runs from the gate at the south-west corner of the park to a point on the northern boundary. The second is at right angles to the first and runs from a point on the first path to the gate at the south-east corner of the park. Each path is a whole number of metres long.
How long are the paths?