Problem
COM-B1-M06-P012 Sum Modulo \(3\)
#12
★★☆☆☆ Level 2 of 5
Numbers are written on a board. In one move, two numbers may be increased by \(1\) and one number decreased by \(2\). Prove that the sum modulo \(3\) does not change.
Compute the change in the sum.
In one move, the sum changes by \(1+1-2=0\). Thus the sum itself is preserved, and therefore its residue modulo \(3\) is preserved.
Sometimes a modular invariant is more than enough.