Henry Ernest Dudeney/Puzzles and Curious Problems/56 - The Ambiguous Clock

Puzzles and Curious Problems by Henry Ernest Dudeney: $56$

The Ambiguous Clock

A man had a clock with an hour hand and minute hand of the same length and indistinguishable.

If it was set going at noon, what would be the first time that it would be impossible, by reason of the similarity of the hands, to be sure of the correct time?

Readers will remember with these clock puzzles there is the convention that we may assume it possible to indicate fractions of seconds.

On this assumption an exact answer can be given.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Clock Puzzles: $56$. -- The Ambiguous Clock
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Clock Puzzles: $48$. The Ambiguous Clock