34

Part of 2013 Harvard-MIT Mathematics Tournament

Problems(1)

2013 HMMT Guts #34: Sums of Multiples of Powers of -1

Source:

For how many unordered sets

\{a,b,c,d\}

of positive integers, none of which exceed

168

, do there exist integers

w,x,y,z

(-1)^wa+(-1)^xb+(-1)^yc+(-1)^zd=168

? If your answer is

A

and the correct answer is

C

, then your score on this problem will be

\left\lfloor25e^{-3\frac{|C-A|}C}\right\rfloor