Henry Ernest Dudeney/Puzzles and Curious Problems/Arithmetical and Algebraical Problems/Clock Puzzles

Henry Ernest Dudeney: Puzzles and Curious Problems: Arithmetical and Algebraical Problems

$56$ - 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?

$57$ - The Broken Clock Face

How may a clock dial with Roman numerals be broken into four parts

so that the numerals on each part add up in every case to $20$?

$58$ - When did the Dancing Begin?

"The guests at that ball the other night," said Dora at the breakfast-table,

"thought that the clock had stopped,

because the hands appeared in exactly the same position as when the dancing began.

But it was found that they had really only changed places.

As you know, the dancing commenced between ten and eleven o'clock.

What was the exact time of the start?"

$59$ - Mistaking the Hands

"Between two and three o'clock yesterday," said Colonel Crackham,

"I looked at the clock and mistook the minute hand for the hour hand,

and consequently the time appeared to be fifty-five minutes earlier than it actually was.

What was the correct time?"

$60$ - Equal Distances

At what time between three and four o'clock is the minute hand the same distance from $\text {VIII}$ as the hour hand is from $\text {XII}$?

$61$ - Right and Left

At what time between three and four o'clock will the minute hand be as far from $12$ on the left side of the dial plate as the hour hand is from $12$ on the right side of the dial plate?

$62$ - At Right Angles

How soon between the hours of five and six will the hour and minute hands of a clock be exactly at right angles?

$63$ - Westminster Clock

A man crossed over Westminster Bridge one morning between eight and nine o'clock by the tower clock

(often mistakenly called Big Ben, which is the name of the large bell only. But this is by the way).

On his return between four and five o'clock he noticed that the hands were exactly reversed.

What were the exact times he made the crossings?