The Quarter-Turn Hands
On an ordinary analogue clock the hour and minute hands move at constant speeds. Counting a full 24-hour day starting at midnight (00:00 inclusive, the following midnight excluded), how many times are the hour hand and the minute hand exactly perpendicular? Give an integer.
Related problems & prerequisites
Worth solving first
- The Hasty Wristwatch 2.0/10
- The Patient Pasture 2.0/10
Source: Classic clock-hand counting exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.