# How often do the hands meet?: visual puzzle | SwaVid

During one complete 12-hour cycle, how many times do a clock's hour and minute hands overlap? See the complete step-by-step solution.

Canonical: https://www.swavid.com/puzzles/clock-overlaps

Source: https://www.swavid.com/puzzles/clock-overlaps

# How often do the hands meet?

## 11 times.

### Compare the speeds

### Each lap is one overlap

### Find the spacing

SwaVid visual puzzle

During one complete 12-hour cycle, how many times do a clock's hour and minute hands overlap?

Detailed solution

The minute hand laps the hour hand a little less than once an hour, so it does not happen 12 times.

In 12 hours the minute hand makes 12 turns and the hour hand makes 1.

The hands meet exactly once every time the minute hand gains a full turn on the hour hand.

The overlaps are evenly spaced, so they happen every 12/11 hours, about 65 minutes 27 seconds.

Answering 12 assumes an overlap every hour, but the one that would be at 11:00 slides to 12:00 and is the start of the next cycle.

- 1 Compare the speeds In 12 hours the minute hand makes 12 turns and the hour hand makes 1. 12 − 1 = 11 laps
- 2 Each lap is one overlap The hands meet exactly once every time the minute hand gains a full turn on the hour hand. 11 overlaps
- 3 Find the spacing The overlaps are evenly spaced, so they happen every 12/11 hours, about 65 minutes 27 seconds. 12 h ÷ 11 ≈ 1 h 5 min 27 s

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