40 identical balls are rolling a straight line. They all have speed equal to v, but some of them might move in opposite directions. When two of them collide they immediately switch their direction and keep the speed v. What is the maximal number of collisions that can happen.

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40 identical balls are rolling a straight line. They all have speed equal to v, but some of them might move in opposite directions. When two of them collide they immediately switch their direction and keep the speed v. What is the maximal number of collisions that can happen. 

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