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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.

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.









That should be all of them.

The third part seems the hardest.


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