I selected five different integer numbers between 1 and 7 (both inclusive) but if I told you their product, you wouldn't be able to deduce whether their sum was odd or even. What is their product?

A solution to this puzzle is to identify the two pairs of numbers of the set of numbers 1 through 7 that have the same product and different (even & odd) sum. Only the following will provide the same products from the given set of numbers:

(1, 6) and (2, 3) with a product of 6 and odd-odd sums [7 & 5]
and
(2, 6) and (3, 4) with a product of 12 and even-odd sums [8 & 7]

Only (2, 6) and (3, 4) satisfy the requirements, therefore the product is 420, i.e., 1*3*4*5*7 or 1*2*5*6*7.

Posted by Dej Mar on 2006-09-21 19:04:23