44 monkeys have a total of 1407 bananas. No two monkeys have the same number of bananas. Show that there is a monkey that has exactly twice as many bananas as another one.

(In reply to re: Solution, sort of... by brianjn)

I'm not sure I understand what you are saying...

What I have done is constructed the smallest possible list of 44 unique integers (beginning with zero) in which no term is double another term.  The sum of this list is 1408.  It is not possible to reduce this sum without including a term which is double one of the other terms - so therefore if the sum is 1407, then one of the terms must be double one of the others.

I don't know how to show a more formal proof of this, although I am confident that it is true.  If you pick any of the 44 terms in the sequence and reduce it by one (to make the sum 1407), it will end up being either the same as or twice as much as one of the other terms.. 

Posted by tomarken on 2006-11-13 20:44:00