Paradoxical Puzzle Pair

Two interesting puzzles, one of which looks hard and is in fact easy, while the other looks easy and is in fact hard.

1. Three Cards

The values attached to a deck of bridge cards start with the Two of Clubs as lowest, with Diamonds, Hearts and Ace of Spades as highest.

If you draw three cards at random from the deck, what is the probability that they will be drawn in order of increasing value? (Answer 1)


2. The Hungry Hunter

A hunter, having run out of food, met two shepherds. One of the shepherd had three loaves of bread and the other had five loaves. When the hunter asked for food, the shepherds agreed to divide the eight identical loaves equally between the three of them. The hunter thanked them and gave them $8. How should the shepherds divide the money? (Answer 2)

• Puzzles and answers from Erwin Brecher’s How Do You Survive a Duel? And Other Mathematical Diversions, Puzzles and Brainteasers (Carlton Books 2018)

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Answer #1: The puzzle sounds far more complicated than it is. The deck of cards is a red herring. The question reduces to this: Take three cards, say 2, 3 and 4 of clubs, facedown. What is the probability of turning them over in the order 2, 3, 4? There are six possible ways of arranging three cards. Therefore the probability is one-sixth.

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Answer #2: It would be wrong to split the money into $3 and $5. Each of the three ended up with 2⅔ loaves. In other words, the first shepherd parted with ⅓ of a loaf and the other shepherd with 2⅓ or 7/3 loaves. The first shepherd should therefore get $1 and the second shepherd $7.

2 thoughts on “Paradoxical Puzzle Pair

  1. Yeah I guessed $3 and $5 on the second puzzle, but that would only be correct if the shepherds gave the hunter all 8 loaves. Maybe the wording (“When the hunter asked for food, the shepherds agreed…”) primed me to think that way, so I didn’t read the rest.

    It’d be interesting to try this puzzle on someone who barely reads English and has to painstakingly decipher every word. They might actually do better because they wouldn’t be able to miss important details.

    • It’d be interesting to try this puzzle on someone who barely reads English and has to painstakingly decipher every word. They might actually do better because they wouldn’t be able to miss important details.

      Yes, apparently so:

      The best font for studying and taking study notes is a harder to read, unfamiliar font researches have shown. Using Comic Sans MS, Bodoni MT, Monotype Corsiva, Haettenschweiler or Comic Sans Italicized significantly improved the student’s performance because they were forced to think harder about the material.

      Difficult fonts for better learning

      And I’ve written about how reading the New Testament in a foreign language increases its power:

      …the Latin of the Gospels is very straightforward. But I still need to think harder than in English, which makes the meaning grow more slowly and powerfully in my brain. I didn’t appreciate the Gospels properly until I read them in Latin and Greek. There are some strange things going on and the Last Supper and Crucifixion are moving stories.

      Criblia

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