Positive integers are written on all the faces of a cube, one on each. At each corner (vertex) of the cube, the product of the numbers on the faces that meet at the corner is written. The sum of the numbers written at the corners is $2004$. If $T$ denotes the sum of the numbers on all the faces, find all the possible values of $T$.

Question

parthkohli · Answer

It's a nice problem though it's elementary and you know how to solve it immediately.

superdavesuper · Answer

there are 6 faces on a cube...so we need to find 6 positive integers to fill. are there any other stipulations such as the 6 integers must be different or consecutive? w/o further stipulations, there may be many sets of possible combinations of integers.

alekos · Answer

@parthkoli, you still there?

superdavesuper · Answer

alright i sucked :( the Q IS solvable as-is. thanx to google, any1 who wants to know, the solution is here: http://www.artofproblemsolving.com/community/c6h77016p442327 be4 clicking though, i recommend writing out the sum n u find the solution urself. good luck :)

alekos · Answer

Thanks Dave. The post corresponds with my solution