How many times are the hands of a clock at right angles (90°) in a 24-hour day?

Problem restatementCount the number of 90° configurations between the hour and minute hands in 24 hours.

Given data

• In 12 hours, hands are at right angles 22 times.

Concept/ApproachRight angles occur twice in most hours, except slightly irregular spacing due to the hour-hand motion. The well-known count is 22 in 12 hours.

Step-by-Step reasoningRight angles in 12 hours = 22Hence in 24 hours = 2 × 22 = 44

Common pitfallsAssuming exactly two per hour (would give 48) and ignoring the skipped/shifted occurrences.