Problem
COM-B1-M06-P014 Residue of Token Sum
#14
★★★☆☆ Level 3 of 5
There are tokens in boxes. In one move, one may add \(4\) tokens to one box and remove \(1\) token from another. Prove that the total number of tokens modulo \(3\) is preserved.
The total changes by \(3\).
In one move, the total number of tokens changes by \(4-1=3\), so its residue modulo \(3\) does not change.
Modular invariant with changing sum.