The product of three consecutive positive integers is exactly eight times their sum. What is the value of the middle number?
5
Let the consecutive integers be n - 1, n, and n + 1. Their sum is 3n, and their product is (n - 1)(n)(n + 1) = n(n^2 - 1). Setting product equal to 8 times the sum gives n(n^2 - 1) = 24n. Dividing by n gives n^2 - 1 = 24, so n^2 = 25, meaning the middle number n is 5.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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