perplexus.info :: Just Math : Possible Values of Expression Evaluation

Possible Values of Expression Evaluation (Posted on 2025-03-27)

Caroline correctly evaluates the expression |(x - y)(y - z)(z - x)| by replacing each of the variables x, y, z with a positive integer. How many possible answers between 1 and 100 (inclusive) could she have gotten?

No Solution Yet Submitted by Danish Ahmed Khan

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and also

Comment 2 of 2 |

I also used computer overkill to find:

[2, 6, 12, 16, 20, 30, 42, 48, 54, 56, 70, 72, 84, 90, 96]

The number in the list is: 15

This sequence is in oeis A088915

"Nonnegative numbers of the form mn(m+n) with integers m,n."

If we call

m = (x - y) and

n = (y - z)

then m+n = (x - y + y - z) = (z - x)

So, the expression is shown to fit the pattern mn(m+n)

Posted by Larry on 2025-03-27 10:17:01

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