(Or: what my brain does while my body swims.)

I have a pack of cards with letters on one side and numbers on the other. I lay out four of them on the table, like this:

**E 6 J 11**

I tell you “Each card with an even number has a vowel on the other side.”

How many cards, and which ones, do you need to turn over to prove me right or wrong? Is it even *possible* to prove me right or wrong from these four cards? For the cards on the table only, or for the whole pack?

Let’s consider **E**. Well, let’s not consider **E** because **E** isn’t worth consideration. The rule doesn’t actually say anything about the other side of a card with a vowel, except that *some* of them have even numbers. Whether **E** has an odd or an even number on the other side doesn’t fall under the scope of the rule.

Do you turn over **6**? Yes, you do, because if it has a consonant on the other side you’ve proven me wrong. Conversely, you need to make sure that **J** doesn’t have an even number because even numbers need vowels. So you turn over **J**.

There’s no need to turn over **11** because the rule doesn’t cover odd numbers at all: whether there’s a vowel or a consonant on the other side of **11** doesn’t matter.

The inverse of my rule is not “Each card with an odd number has a consonant on the other side” but “Each card with a consonant has an odd number on the other side”. Cards with vowels can have odd or even numbers; cards with odd numbers can have vowels or consonants.

Interestingly, it’s possible that you’ll prove me wrong for the whole pack from these four cards: if **6** should have a consonant, or **J** an even number. You can’t prove me right for the whole pack; for that you need to check all even-numbered and all consonant cards in the pack. You can, of course, prove me right for only the cards on the table from the cards on the table.

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