This clock puzzle asks: if the time is exactly 3:15, what is the smaller angle between the hour hand and the minute hand?
The correct answer is 7.5 degrees.
At 3:15, the minute hand points directly at the 3, which is 90 degrees from 12. But the hour hand does not stay exactly on the 3. During those 15 minutes, it has moved one quarter of the way toward 4.
The hour hand moves 30 degrees per hour, so in 15 minutes it moves 7.5 degrees. That puts it at 97.5 degrees from 12.
The difference between 97.5 degrees and 90 degrees is 7.5 degrees. That small movement of the hour hand is the part many people forget.
