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.

(In reply to Kool sets by harold reiter)

As much as I'd like to take credit for it... it's not mine.

I will direct you to:

http://www.stetson.edu/departments/mathcs/events/mathcontest/1995/index.shtml

where I found this problem.

Posted by SilverKnight on 2004-12-21 21:43:32