Henry Ernest Dudeney/Modern Puzzles/83 - A Critical Vote

Modern Puzzles by Henry Ernest Dudeney: $83$

A Critical Vote

A meeting of a charitable society was held to decide whether the members should expand their operations.

It was arranged that during the count those in favour of the motion should remain standing,

and those who voted against should sit down.

"Ladies and gentlemen," said the chairman in due course, "I have the pleasure to announce that the motion is carried by a majority exactly equal to exactly a quarter of the opposition."

"Excuse me, sir," called somebody from the back, "but some of us over here could not sit down, because there are not enough chairs."

"Then those who wanted to sit down but couldn't are to hold up their hands ... I find there are a dozen of you, so the motion is lost by a majority of one."

Now, how many people voted at that meeting?

Note that the language and concepts have been updated to accommodate modern sensibilities.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $83$. -- A Critical Vote
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $166$. A Critical Vote