If a + b + c = 31, where a, b, c are distinct integer. What is the maximum value of a × b × c?

<p>The sum of three numbers is given; the product will be maximum if the numbers are equal.</p><p>So, if a + b + c is defined, abc will be maximum when all three terms are equal. In this instance, however, with a, b, c being distinct integers, they cannot all be equal. So, we need to look at a, b, c to be as close to each other as possible.</p><p>a = 10, b = 10. c = 11 is one possibility, but a, b, c have to be distinct. So, this can be ruled out.</p><p>The close options are, </p><p>a, b, c = 9, 10, 12; product = 1080</p><p>a, b, c = 8, 11, 12; product = 1056</p><p>Maximum product = 1080</p>

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