# 9.3. (7 points)

On a circular track 60 cm long, ants are moving in both directions at a speed of 1 cm/s. When two ants collide, they instantly turn around and continue moving at the same speed in opposite directions. It turned out that 48 pairwise collisions occurred in one minute. How many ants could have been on the track?
Answer: 10 or 11 or 14 or 25.

Solution: Note that the situation will not change if we assume that after colliding, the ants continue their movement without changing direction or speed. Suppose two ants collide, then 30 seconds after this, each of them will have crawled half the circle and they will collide again.

Therefore, each such pair will have exactly 2 collisions per minute. Thus, if $x$ ants are crawling in one direction and $y$ ants in the opposite direction, then $2xy=48, xy=24$. Therefore, the desired quantity $x+y$ can take the values: $1+24=25, 2+12=14, 3+8=11$, $4+6=10$.