Question 173
Umberto and Doisberto play on a $3 \times n$ board by placing dominoes, always covering two adjacent squares (sharing a side) of the board. Umberto makes the first move, Doisberto makes the second, and they continue playing alternately. The player who cannot move loses. For each of the cases below, say which of the players can devise a strategy that always guarantees victory regardless of how the other one plays.
a) $n=3$
b) $n=4$
a) $n=3$
b) $n=4$