In a coalitional game n miners find equal blocks of gold. Two can carry one piece home. The payoff of a coalition S is $\nu(S)=|S|/2$ if $|S|$ even and $(|S|-1)/2$ for $|S|$ odd.
Determine the core if n is even, that is the set of imputations $x$ such that $\sum_{i\in S}x_i\ge \nu(S)$ for all S.
Could someone show how to do this systematically? What if three miners can carry one lump?