# Which card(s) needed to be turned?

There are 4 cards like below on the table:

Every card has a letter on one side, and a number on the other side. The cards on the table as like above.

Moreover, it is given you that

If there is a odd number on one side, the letter on the other side has to be consonant.

So

To make sure all cards are under this odd-consonant rule, at least which card/cards needed to be turned?

• I'm not sure I understand - do we have to verify that all 4 cards follow the rule? Sep 30, 2017 at 19:52
• @thecoder16 you will turn the least amount of cards to be sure they are under the rule.
– Oray
Sep 30, 2017 at 19:53
• Are we given which letters/numbers that could be on the other side? Or could any number/letter be on the other side? If so, then we would just have to flip all the cards with odd numbers and consonants, no? Sep 30, 2017 at 19:54
• @thecoder16 any number or letter, and it is what is asked in the question :)
– Oray
Sep 30, 2017 at 19:55
• This puzzle could do with being made a bit clearer. I had to re-read it and the comments a couple of times before I understood, and it seems I'm not the only one who had trouble. Additionally, the way it is worded I was tempted to post a pedantic answer and say none: it is "given" that if there is an odd number on one side, the letter on the other side has to be a consonant, so there is nothing to check. This is a logic puzzle after all, so it's best to be precise if you want to avoid valid answers that you didn't intend! Oct 1, 2017 at 1:19

I think that the cards that need to be flipped are

The yellow(A) and orange(1) cards. The yellow(A) one needs to be flipped to check if the number on the other side isn't odd, because otherwise there would be an odd number with a vowel, breaking the rule. The orange(1) one needs to be flipped to see if the other side has a consonant to follow the rule. The pink(B) one doesn't need to be flipped since if the other side's number is odd-it follows the rule. If it is even, there is no rule that needs to be followed. The same logic applies for the blue(2) one-there is no rule about even numbers.

• @humn, ok, i can add that :) Sep 30, 2017 at 21:14

We have the rule:

One side is odd $\implies$ other side is a consonant.

So:

This means we must turn the orange (1) card to check if the other side is a consonant. We do not have to turn the blue (2) card as we have not been told what to expect if we do. The yellow (A) card is a vowel, and by the rule, the other side CANNOT be an odd number, so we need to check this. Finally, the pink (2) card is an even number, and again we have no rule to determine the other side against.

In a nutshell:

Odd $\implies$ consonant $\equiv$ vowel $\implies$ even.

You need to turn card "1" in order to prove that there is a consonant on the other side. Then you have to turn card "A" in order to prove that there is NOT an odd number on the other side. Turning the other cards is unnecessary as the is not a rule saying what mist be on the other side of an even number, or what must be on the other side of a consonant. This last bit is the tricky part. Many people assume that as an odd number must have a consonant on the other side, a consonant must ALWAYS have an odd number on the other side, but this is not stated.