Question 72
Numbers $1, 2, 3, \ldots, 60$ are written in a row (in this order). Igor and Ruslan take turns in making moves; Igor starts; by one move the player puts one of the signs of operation $+$, $-$, $\times$ between some pair of adjacent numbers. When a sign is placed between every two adjacent numbers we calculate the value of the obtained expression. Igor wins if this value is divisible by $3$, otherwise Ruslan wins. Determine who of the two players has a winning strategy.