Problem
COM-B1-M12-P018 Set 5. Number 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?
Residue modulo \(3\).
Both changes are divisible by \(3\), so the residue modulo \(3\) is invariant. \(5\equiv2\pmod3\), while \(100\equiv1\pmod3\). Impossible.
Residue invariant.