$\underline{\text { Folklore }}$

Five identical balls are moving in one direction along a straight line, some distance apart from each other, while five other identical balls are moving towards them. The speeds of all the balls are the same. When any two balls collide, they fly apart in opposite directions with the same speed they had before the collision. How many total collisions will occur between the balls?
After the collision, the balls scatter at the same speed, so the situation will not change if we allow the balls to pass through each other upon collision, maintaining their speed. Then each ball rolling "to the right" will meet each of the balls rolling "to the left" once, meaning there will be 25 encounters.

## Answer

25 collisions.