Math (Combinatorics)
posted by Shin .
40 students attended the brilliant summer camp at Stanford University. "k" of the students at the camp are working on math problems and the others are working on nonmath problems. One of the camp mentors noticed that whenever all the students were partitioned into 2 or more groups of equal size, they could never have the same number of math students in every group. How many different values could "k" have?

16

Two thin and identical steel rods move with equal speeds v=1 m/s in opposite directions and collide longitudinally.The collision is perfectly elastic and the rods swap their velocities. How long does the collision last in seconds if the length of the rods is l=30 cm. Assume that the speed of sound in the steel rods is c=5000 m/s?