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.

Imagine there are enough 1's to make the sum 100.  The key is the 100 product.

{2,2,5,5,1,1,1...

{2,5,10,1,1,1...

{10,10,1,1,1...

{4,25,1,1,1...

{2,2,25,1,1,1...

{4,5,5,1,1,1...

{2,50,1,1,1...

{5,20,1,1,1...

That should be all of them.

The third part seems the hardest.

-Jer

Posted by Jer on 2004-11-15 14:28:22