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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 Second part | Comment 2 of 10 |

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
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