You have an odd number of tokens whose weights are known whole numbers, and they don't all have the same weight. Show that there's a token you can remove so that the remaining tokens can't be split into two equal-size sets that have the same total weight.
Mathier bonus questions:
The weights are instead positive rational numbers.
The weights are instead positive real numbers.
Show that this doesn't necessary hold for an Abelian group, where weights are non-identity elements that are summed with the group operation.