In order to fully improve the efficiency and minimize the time, you can brush two boards at the same time, because it takes 2 minutes to brush one side and 2 minutes to brush two boards at the same time.

Brush two of the three boards at the same time. After 2 minutes, put one board aside, turn the other board over, and brush the paint with the third board at the same time.

After another 2 minutes, the first board will be completely brushed, and the last one will be turned over and painted with the board placed on one side;

In two minutes, all three boards will be brushed.

The time for three boards is 3*2=6 (minutes).

So it takes at least 6 minutes to brush three boards.

Extended data:

This kind of problem belongs to the pancake problem in mathematics, and the formula of pancake problem is:

Total time = number of cakes × 2÷ the quantity of each pot × the time to bake each side.

When the time is not an integer, the approximate number is taken by the method of entering one.

For example, when the number of cakes is 4, the number of sheets in each pot is 3, and each side is baked for 2 minutes, according to the formula, 4×2÷3×2≈6 points.

When only two cakes can be baked in one pot: total time = time to bake one side × number of cakes.