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.

I've found {7,4,4,1,1, .....} and {100,2,1,1,1...}.  Perhaps somebody can write a computer program and see if there are any others.

I'm pretty clear that there are at least 94 1's in the set, so 6 nested loops ought to do it.

Posted by Steve Herman on 2004-11-15 17:41:24