Hard problem - dividing the subs !! 1. The problem statement, all variables and given/known data Anupam brought n > 0 subs, one each of length 1; 2; 3;....... ; n, to a grading party. The three TAs distributed the subs among themselves such that no sub was broken, and each TA ended up with an equal total length. For what values of n is such a division possible? 2. Relevant equations At some point, we may use the the sum formula : n(n+1)/2 3. The attempt at a solution I tried finding a pattern n = 1 we have only one sub, doesn't work n= 2 doesn't work n=3 doesn't work, as we can't divide this by 3 people. n=4 doesn't work, n= 5 it works !! we have 1,2,3,4,5 we can divide by 3 as follows : one of the TAs will take 5 The other will take 4,1 The third will take 2,3 So, how should I precede with that ? Do you think this is the right thing ?