It's very boring to look at a black-and-white clock face, so Clive painted the number 12 red at exactly noon and decided to paint the current hour red every 57 hours.

a) How many numbers on the clock face will end up being painted?

b) How many red numbers will there be if Clive paints them every 1913 hours?
a) Since GCD $(12,57)=3$, every third hour will be red: 12, 3, 6, and 9 o'clock.

b) Since GCD $(12,1913)=1$, all numbers on the clock will turn red. (This will happen, however, almost after 3 years.)

## Answer

a) 4 numbers; b) all 12 numbers.