Enigma 1120: Assorted numbers
10 April 2017
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From New Scientist #2276, 3rd February 2001 [link]
Consider the five-digit and six-digit numbers represented by the words MELONS, PLUMS, APPLES, LEMONS and BANANA, in which different letters stand for different digits but the same letter always stands for the same digit whenever it appears.
If the product 2 × MELONS is greater than the product 35 × PLUMS, but less than the product 3 × APPLES; and if the product 99 × LEMONS is greater than the product 16 × APPLES, but less than the product 210 × PLUMS, then how big is a BANANA?
Thanks to Hugh Casement for providing the source for this puzzle.