A collection of positive integers (not necessarily distinct) is called Kool if the sum of all its elements equals their product.

For example, {2, 2, 2, 1, 1} is a Kool set.
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a) Show that there exists a Kool set of n numbers for all n>1

b) Find all Kool sets with sums of 100

c) Find all Kool sets with 100 members.

{1, 1, ..., 1, 1, 2, n} with n-2 1's adds and multiplies to 2n. Therefore, it is a cool set with n numbers.

Posted by Math Man on 2014-05-12 17:46:00