# Puzzle 1 – Deductive Reasoning

This is a logic problem called the Wason 4-card selection problem. In the original study about 60% of people chose to turn over cards ‘D’ and ‘5’ (answer E). Only 5% chose to turn over the ‘D’ and ‘2’ cards (answer ‘F’) – the correct answer! This is a ‘counter-intuitive’ problem for many of us, and understanding why we got it wrong should help our logical thinking.

### Mindware Tips

One trick in solving this problem is to look for situations in which the rule might be broken. If you turn over the ‘D’ and there was an even number on the other side then the rule would be untrue. So you need to turn over the ‘D’.

What about ‘A’? The rule doesn’t say anything about what number should be on the other side of a vowel, so we can ignore this card.

Now imagine what might be on the back of the ‘2’ card. If it was a consonant (e.g. another ‘D’), then the rule would be broken! So you do need to turn over the ‘2’ card to ensure that the rule is true.

What about the ‘5’ card? What if there was a vowel (e.g. an ‘A’) on the other side? You might think that this would disprove the rule we want to test, but it does not. ‘If P then Q’ does not mean the same is ‘If Q then P’. ‘If there is a consonant there is an odd number’ does not imply ‘If there is an odd number there is a consonant’ – no more than ”If there is rain there is water’ does not imply ‘If there is water there is rain’. So a 5/A card is consistent with the rule ‘If there is a consonant on one side, there is an odd number on the other’.