induction – Math/Logic Puzzle – Mathematics Stack Exchange

Anybody have any insight on how to solve this problem? My friend asked me about it and it’s been bothering me for a few days. I tried to approach it by induction (the base case with two people is straightforward, but I got stuck on the inductive step). Anyway, I thought it was a fun problem and was curious how to approach it. Any tips on possible solutions would be lovely!

Some people stand in a circle exchanging pieces of chocolate. Each of them starts with an even number of chocolates (the numbers might be different between different people). Every minute, each of the people passes half their chocolates to the person to their right. If anyone ends up with an odd number of chocolates, they take an extra chocolate from a jar in the center. Prove that regardless of the initial distribution of chocolates, after a finite number of steps everyone ends up with an equal number of chocolates.