A clock is a complicated measuring device. There are two scales superimposed on each other, one for hours and one for minutes.

On this clock, the hours are numbered and there are marks for each minute. Those of us who can tell time know that even though the minute hand is on the 6, is it 30 minutes, not 6 minutes past the hour. Since the hour hand is between 3 and 4, we know that the time is 3:30.

For this month’s puzzle we need to introduce an idea, the “minute position” of the hour hand. At 3:30, the minute position of the hour hand is 17 ¹/₂ minutes. That is, the hour hand is pointing at the 17 ¹/₂-minute mark on the clock face.

At 3:12, the minute position of the hour hand is 16 minutes.

Now for the puzzle:

1. At what time between 3 o’clock and 4 o’clock is the minute hand 18 minutes ahead of the hour hand?

2. At what time between 3 o’clock and 4 o’clock is the minute hand 18 minutes behind the hour hand?

Try your luck, then check our solution.

Thanks to David Tempel for suggesting this month’s puzzle

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