Question 139
There is a set of $n$ coins with distinct integer weights $w_1, w_2, \dots, w_n$. It is known that if any coin with weight $w_k$, $1 \le k \le n$, is removed from the set, the remaining coins can be split into two groups of the same weight. (The number of coins in the two groups can be different.) Find all $n$ for which such a set of coins exists.
(This problem was suggested by Gregory Galperin.)
(This problem was suggested by Gregory Galperin.)