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Kool Numbers (Posted on 2004-11-15) Difficulty: 4 of 5
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.

No Solution Yet Submitted by SilverKnight    
Rating: 3.0000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts First part | Comment 1 of 10
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
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