



 
Thomas, When solving any mathematics problem, one must state it in such a way that all the details are clear. Here is my interpretation of your question: You are to distribute the given numbers into two groups with the product of the numbers in the first group equal to K and the product in the second group equal to L. The question asks if you can arrange the groups so that K = 2*L. If that is indeed the question, then the answer is pretty easy. The number of 2's in the factorization of one group must be even, the number of 2's in the other factorization must be odd. Chris Thomas replied
Nice! Suppose that you have numbers A and B such that A/B = 2. What is A+B in terms of B? Is this possible? Hint: how do you test a long number to see if it is divisible by 3? How does this generalize to two big numbers that have a sum divisible by 3? Good Hunting!
 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 