Hands pointing towards each other per day: How many times in a day do the hands of a clock point towards each other (coincide)?

Introduction / Context:
The hands coincide 11 times in 12 hours (not 12, since the minute hand “laps” the hour hand slightly less than once per hour). Over a full day, this doubles to 22 coincidences.

Given Data / Assumptions:

• Standard analog 12-hour cycle.
• Uniform hand motion.

Concept / Approach:
Use the standard count of overlaps per 12 h and multiply by 2.

Step-by-Step Solution:

Verification / Alternative check:
Average interval between overlaps is about 65 5/11 minutes; 24 h / (65 5/11 min) ≈ 22.

Why Other Options Are Wrong:
24 and 12 assume one per hour or one per 2 hours incorrectly; 20 undercounts.

Common Pitfalls:
Assuming exactly once per hour; the hour hand moves steadily, so the minute hand cannot lap exactly 12 times in 12 hours.

Final Answer:
22