RIOPLATENSE 1996 Problem 5

There is a board with $n$ rows and $4$ columns, and white, yellow and light blue chips. Player $A$ places four tokens on the first row of the board and covers them so Player $B$ doesn't know them. How should player $B$ do to fill the minimum number of rows with chips that will ensure that in any of the rows he will have at least three hits?

Clarification: A hit by player $B$ occurs when he places a token of the same color and in the same column as $A$ .