# mistakes in analogous puzzles from The Tipping Point

In the book 'The Tipping Point', Malcolm Gladwell cites two puzzles and draws an analogy between them, in fact he claims the two are equivalent. I believe there are some problems with both puzzles, and the analogy as well. Do you see the same problems, and are there any suggestions to fix this?

The first riddle:

Consider the following brain teaser. Suppose I give you four cards, labeled with the letter A and D and the numerals 3 and 6. The rule of the game is that a card with a vowel on it always has an even number on the other side. Which of the cards would you have to turn over to prove this rule to be true? The answer is two: the A card and the three card. The overwhelming majority of the people given this test, though, don't get it right. They tend to answer just the A card, or the A and the 6. It's a hard question.

Here, the D-card should be turned over as well, as there is no indication that cards cannot have letters on both sides.

And now the second:

But now let me pose another question. Suppose four people are drinking in a bar. One is drinking Coke. One is sixteen. One is drinking beer and one is twenty-five. Given the rule that no one under twenty-one is allowed to drink beer, which of those people's IDs do we have to check to make sure the law is being observed? Now the answer is easy, in fact, I'm sure that almost everyone will get it right: The beer-drinker and the sixteen-year-old. But, as the psychologist Leda Cosmides (who dreamt up this example) points out, it is exactly the same puzzle as the A, D, 3 and 6 puzzle. The difference is that it is framed in a way that makes it about people, instead of about numbers, and as human beings we are a lot more sophisticated about each other than we are about the abstract world.

But checking the ID of the sixteen-year-old doesn't make sense, you already know his age. He can still be drinking tequila while you read his birth-date.

The analogy is incorrect after these mistakes. If those two mistakes are fixed, by adding the rule 'Cards always have a letter on one side and a number on the other' to the first puzzle, and in the second case alter the wording so that we may also check the drink of the sixteen-year-old, the analogy is correct, right?

Yes, you are correct. Those mistakes should be fixed in order to make the questions analogous.

The second riddle seems to be badly worded. The first one is correct as it is, though. In order to check that a card with a vowel on one side always has an even number on the other side you have to check two cards. The first one is obvious: in case the A card doesn't have an even number on the other side the rule is proven wrong. Then you have to check the "3" card for pretty much the same reason: if there is a vowel on the other side the rule is proven wrong again. Checking the remaining two cards is useless as there is not a rule saying what's on the other side of a consonant - D - or what's on the other side of an even number - 6. Remember that there is only one rule: if a card has a vowel on one side there must be an even number on the other side. Hope this helps.

• I think you misunderstood the objection to the first riddle. Suppose the card with a D visible had an E on the other side. Then the rule "a card with a vowel on it always has an even number on the other side" is violated, because the card with an E on one side has a D on the other side. The proposed fix is to specify that all cards have a letter in one side and a number on the other, which would prevent this scenario. – isaacg Nov 22 at 8:25
• I guess you are right. Thanks! :) – fabs Nov 25 at 10:11