A clockmaker's apprentice fitted two identical hands — and broke every reading
An apprentice repairing a clock accidentally fits two hands of identical length and appearance, so there's no way to tell which is the hour hand and which is the minute hand just by looking. At certain moments, the two readings you could take from that single hand position are both valid — and genuinely different — clock times. How many such ambiguous moments occur in a 12-hour period?
Reveal the answer
132 times in 12 hours, forming 66 distinct ambiguous pairs — this excludes the 11 moments the hands exactly overlap, since swapping two identical overlapping hands changes nothing. Boris Kordemsky posed this as 'The Wondrous Clock' in The Moscow Puzzles, and it remains a favourite because solving it means tracking two independently moving hands rather than just one.