How many times in a day are the hands of a clock in a straight line but opposite in direction?

Problem restatementCount how often, in 24 hours, the hands are collinear with 180° between them (opposite direction).

Concept/ApproachIn any 12-hour span, the hands are opposite exactly 11 times (roughly every 65 5/11 minutes offset by half a cycle). Over 24 hours, this doubles.

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

Common pitfalls

• Including overlaps (0°) as well; the question asks for opposite direction (180°) only.

Final Answer22 times