Monday, December 14, 2009

Some Logic Puzzles

1) Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

A) Yes       B) No       C) Cannot be determined

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2) Suppose four cards are placed on a table. Each card has a letter on one side and a number on the other. The visible sides of the cards are the following:

A     K     8     5

Two of the cards are letter-side up, and two of the cards are number-side up. The rule to be tested is this: for these four cards, if a card has a vowel on its letter side, it has an even number on its number side. Your task is to decide which card or cards must be turned over to find out whether the rule is true or false. Indicate which cards must be turned over.

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(taken from "Rational and Irrational Thought: The Thinking That IQ Tests Miss")

7 comments:

Parisa said...

Fun! I saw the first one recently in an online article and was surprised by how many people got this wrong.

Queen of the Bongo said...

1) Yes 2) Only one card, the one with the A.

What do I win?!

Yisong said...

Your first answer is correct, but not the second one =)

Lance said...

Won't both the "A" card and the "8" card have to be turned over to determine if the rule is true? The "K" card and the "5" card are irrelevant to the vowel <-> even number connection, aren't they?

Yisong said...

Close, but not quite, Lance. The statement isn't a bi-directional implication.

And in fact, if it actually was a bi-directional implication, then you'd have to turn over all four cards.

Lance said...

I see. If vowel, then even number, but not necessarily the other way around.

So it's one card, and the "8" card, then, because the condition has to be tested with the desired result known?

Yisong said...

I prefer to convert it into propositional logic. Let E denote the event that that the number side of the card is even, and let V denote the event that the letter side of the card is a vowel. And for event E, let ~E denote the negation of the event (i.e., the number side is odd).

Then we can write the statement as:

V IMPLIES E

which is equivalent to

~V OR E

which you can check by writing out and inspecting the truth tables for both. Intuitively, if the letter side isn't a vowel, then ~V is true and the statement is true vacuously.

The only time when the statement can be false is when the letter side is a vowel and the number side is odd. As such, you need to flip over A and 5 in order to verify that the rule is satisfied for the four cards.