EngIntoHW,
The smallest time is zero if you set the ants at the ends of the board and facing away from the center. In no time at all, they walk off the board.
The longest time is one minute if you set the ants at the ends of the board facing the center. It doesn't matter what the count is or how you distribute the ants, both groups will take one minute to drop off the board. When the two groups collide in the center of the board, the group members will change as described below. This is analogous to conservation of momentum for identical masses such elastic pool balls traveling at the same speed.
Take the case of two pool balls traveling in opposite directions and colliding. We initially have 1>--<2 before and after <1--2> . We still have 2 groups of 1 ball each going in the same direction, but the membership changed. Now consider an asymmetric group like the following coming together 1,2,3 >--<4,5 . Afterwards it will be <1,2--3,4 5> . After the collision, we will still have a group of three balls going from left to right and a group of 2 balls going from right to left according to the conservation of momentum. But again the membership of the group changed.
That shows that some of the ants will end up at the opposite end of the board and drop off and others will reverse at the center of the board and drop off at where they started. In both cases it will take one minute for each ant to drop, and they all will drop at the same time.
Ratch