So it seems that there are some math people around. To follow up on http://www.wallstreetoasis.com/forums/harder-brain... here is another one:
Requires middle school math, but sure can ruin an interview.
As before, SBs for 1st correct answer.
Edit - all numbers are strictly positive. Apologies for confusion, but the problem remains open.
Edit - To provide an update, this has, thus far, been proven in 1 confirmed way by nonTargetChimp 9 (see his text file proof), and also in 1 more way that appears correct by unForseen (or rather by a friend of unForseen that works in HR). Another proof using trigonometry has been proposed and has not been fully evaluated but could be correct, and blastoise tried to prove this using fancy linear algebra but so far that proof does not appear to be correct, since he was able to prove it ignoring the positive constraint, meaning he proved something that is false. The most elegant solution to date, in my opinion, would have to be the HR rep's as presented by unForseen, which is found on page 8.
Background on the problem - came from an 8th grade city level math competition from the late 1960s at a mathematical school in the USSR.