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.
__________________________________

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.

The set {P,2,1,1,...1} with (P-2) 1's is Kool, and has P terms. The first such sets are
{2,2},
{3,2,1},
{4,2,1,1},
{5,2,1,1,1},
{6,2,1,1,1,1}...

Posted by Federico Kereki on 2004-11-15 13:48:02