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

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?

Solution

$12:05 \tfrac 5 {143}$, where it cannot be distinguished from $01:00 \tfrac {60} {143}$.

Proof

See Ambiguous Times for full analysis.

$\blacksquare$

Sources

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