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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 painted?

b) How many red numbers will there be if Clive paints them every 2005 hours?
a) Since GCD $(12,57)=3$, every third number will be red: $12,3,6$ and 9.

b) Since GCD $(12,2005)=1$, all numbers on the clock will be red. (This will happen, though, almost after 3 years.)

## Answer

a) 4 numbers; b) all 12 numbers.