# Math (Combinatorics)

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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 non-math 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?

• Math (Combinatorics) -

16

• Math (Combinatorics) -

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?

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