Alcohol Problem

Fill one glass with wine and another with water. Transfer a teaspoonful of wine from the first glass into the second. Then transfer a teaspoonful of that mixture back into the first glass. Now, is there more wine in the water or water in the wine?

Most people will predict it’s the former, but in fact the two quantities will always be the same. Can you see why?

A Weighty Problem

“Here is a quaintly told problem in mechanics, which, despite its apparent simplicity, is said to have caused Lewis Carroll considerable disquietude,” writes Sam Loyd in his Cyclopedia of 5000 Puzzles, Tricks, and Conundrums (1914). He quotes Carroll:

If, to a rope, passed over a loose pulley, is suspended a ten-pound counter weight, which balances exactly with a monkey eating an apple, swinging at the other end, what would be the result if the monkey attempts to climb the rope?

“It is very curious to note the different views taken by good mathematicians,” Carroll noted. “Price says the weight goes up with increasing velocity. Both Clifton and Harcourt maintain that the weight goes up at the same rate of speed as the monkey; while Sampson says that it goes down.”

So which is it? Be warned, Loyd’s thinking is inconclusive.

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Zebra Puzzle

This puzzle has been attributed both to Lewis Carroll and to Albert Einstein:

  1. There are five houses in a row. Each of the houses is painted a different color, and their occupants come from different countries, own different pets, drink different beverages, and smoke different cigarette brands.
  2. The Englishman lives in the red house.
  3. The Spaniard owns the dog.
  4. Coffee is drunk in the green house.
  5. The Ukrainian drinks tea.
  6. The green house is immediately to the right (your right) of the ivory house.
  7. The Old Gold smoker owns snails.
  8. Kools are smoked in the yellow house.
  9. Milk is drunk in the middle house.
  10. The Norwegian lives in the first house.
  11. The man who smokes Chesterfields lives in the house next to the man with the fox.
  12. Kools are smoked in the house next to the house where the horse is kept.
  13. The Lucky Strike smoker drinks orange juice.
  14. The Japanese smokes Parliaments.
  15. The Norwegian lives next to the blue house.

Who drinks water? Who owns the zebra?

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Diophantus’ Age

No one knows much about Diophantus, the Greek mathematician, but in the sixth century a math puzzle purported to give his epitaph:

“This tomb holds Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father’s [total] life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life.”

At what age did he die?

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The Kayaker

A child releases a toy boat in a stream that flows at 3 miles an hour. At that instant, a kayaker 14 miles downstream begins paddling upstream at 7 miles per hour. How long will it take him to reach the toy?

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