“The Barrel Puzzle”


From Amusements in Mathematics by Henry Ernest Dudeney (1917):

The men in the illustration are disputing over the liquid contents of a barrel. What the particular liquid is it is impossible to say, for we are unable to look into the barrel; so we will call it water. One man says that the barrel is more than half full, while the other insists that it is not half full. What is their easiest way of settling the point? It is not necessary to use stick, string, or implement of any kind for measuring. I give this merely as one of the simplest possible examples of the value of ordinary sagacity in the solving of puzzles. What are apparently very difficult problems may frequently be solved in a similarly easy manner if we only use a little common sense.

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Some years ago there was a cat-concert held in Paris. It was called ‘Concert Miaulant,’ from the mewing of the animals. They were trained by having their tails pulled every time a certain note was struck, and the unpleasant remembrance caused them to mew each time they heard the sound again.

— Frank H. Stauffer, The Queer, the Quaint and the Quizzical, 1882

A Modest Proposal

Okay, I’ll ask three questions, and if you miss one I get your house. Fair enough? Here we go:

  1. A clock strikes six in 5 seconds. How long does it take to strike twelve?
  2. A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?
  3. A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?

Don’t be hasty — your house is on the line.

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