Problem
COM-B1-M11-P018 Sum on a Board
#18
★★★☆☆ Level 3 of 5
The number \(5\) is written on a board. In one move, one may add \(6\) or subtract \(9\). Can \(100\) be obtained?
Look at the residue modulo \(3\).
Both changes are divisible by \(3\), so the number modulo \(3\) is invariant. Initially \(5\equiv2\pmod3\), while \(100\equiv1\pmod3\). Therefore \(100\) cannot be obtained.
Residue invariant.