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How many times do the hands of a clock coincide (overlap) in a 24-hour day?

Difficulty: Easy

Correct Answer: 22 times

Explanation:

Problem restatement
Count the number of overlaps of the hour and minute hands in 24 hours.


Concept/Approach
In 12 hours, the hands coincide 11 times (not 12), due to the hour hand's continuous motion. Therefore, in 24 hours they coincide twice that.


Step-by-Step reasoning
Coincidences in 12 hours = 11Hence in 24 hours = 2 × 11 = 22


Common pitfalls
Assuming one overlap per hour (would give 24) instead of 11 per 12 hours.

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