Proving that cows have same weight without weighing it! My friend gave me this problem and I have no clue how to go about it:
A peasant  has $2n + 1$ cows. When he puts aside any of his cows,
the remaining $2n$, can be divided into two sub-flocks of $n$ cows and each having
the same total weight. How can we prove that the cows all have the same weight? 
How can I approach this?

We have $2n+1$ equations in $2n+1$ unknowns. This has a unique solution. As all the cows having the same weight is a solution, it is the only solution.
