To make ends meet, vatsin is diving for coins on the ocean floor. he finds 2n+1 coins in total, n ∈ n, each with an arbitrary natural number value. the coin values are not necessarily distinct. unfortunately, his hands are small and he can only carry 2n coins back to the surface. prove that it is possible for vatsin to surface with 2n coins such that the total value of his earnings is divisible by 2n .