Puzzles

Can You Solve This Logic Puzzle? It Seems Incredibly Easy But May Reveal A Cognitive Bias

The Wason Card Selection Task

Can you solve this logical problem?

Make a mental note of your answer. The correct answer is given below.

Intelligence & Cognitive Biases

“A global concept that involves an individual’s ability to act purposefully, think rationally, and deal effectively with the environment.” D. Wechsler

Our ability to think rationally and deal effectively with the environment to attain our purposes is often impaired by limitations in our cognitive processes. We have built in ‘cognitive biases’ that work against rational thinking, leading us to faulty conclusions, judgments and decisions.

Understanding these biases is generally held back by our lack of awareness of the inner workings of our own minds. Cognitive psychologists have found that we have no conscious experience of most of what happens in our minds. Conscious awareness and control is in fact just the tip of an iceberg of cognitive functions associated with perception, memory and information processing. Most of what we process goes on ‘below the radar’.

The cognitive biases that are built into our thinking processes are revealed through carefully designed experiments.  One of these experiments you’ve just experienced – the Wason Card Selection Task. It looks at our ability to reason logically with ‘if….then’ conditional statements.

The Answer to the Puzzle

The correct answer to the Wason Card Selection task is:  D and 2.

Here’s why:

The underlying logical rule is ‘If x then y’ (where x is the letter D and y is the number 5).

So if the D doesn’t have a 5 on the other side it would break the rule.

You know that each card has a letter on one side and a number on the other, so the second card ‘A’ has to have a number on the other side. If there is a 5 on the other side (or any other number), that doesn’t invalidate the rule. After all, the rule does not say that ONLY the letter D has a 5 on the other side.  ‘If x then y’ is perfectly consistent with ‘If p then y’ and ‘If q then y’ and ‘If r then y’ and so on.

What about the 2 card?  If you turn this over and it has a D on the other side, that would break the rule. Here would be a card that shows ‘If x then not y’. This clearly violates the rule we’re trying to test. If you don’t turn this card over you won’t know for sure whether the statement you’re testing is true or not.  So you have to turn this card over!

What about the 5 card?  A lot of people choose this card – but this choice is actually a mistake!  ‘If there is a D on one side there is a 5 on the other’ does not imply ‘If there is a 5 on one side there is a D on the other’. (‘If x then y’ does not imply ‘If y then x’). It only works one way.  ‘If there’s a solar eclipse bats leave their caves’ does not imply ‘Bats leave their caves therefore there’s a solar eclipse’. Bats might leave their caves because it’s simply night time!

So turning over the 5 card won’t tell you anything useful!

The Cognitive Biases this Puzzle Demonstrates

There are two cognitive biases here that catch a lot of people out.

First is an error in our logical reasoning. We tend to assume that ‘If x then y’ also means ‘if y then x’. But this is wrong as the bat example shows. You just need to find one counter example like this to test your logical assumptions!

Second, even if we have our logic correct, we tend not to look for information that proves us wrong. This may explain why many people do not turn over the 2 card. We are biased to look for information that confirms beliefs rather than information that disconfirms them.

Who Gets This Wrong? Who Gets This Right?

Did you get the correct answer?  If not, you’re in a big majority.

In the original study, about half the participants in the experiment make the mistake of turning over the D and 5 cards.  Another 33% make the mistake of only turning over the D card. Only 4% of participants correctly select the D and 2 cards!

If you look at the 4% who get it right, what makes them different? The answer – to a large extent – is their intelligence level. It has been found that more intelligent people are generally less prone to these cognitive biases that distort their reasoning.

I am currently doing studies looking at the effect of improving intelligence on solving these sorts of problems. Back in 2008 it was found that there does in fact exist a training exercise that increases IQ substantially. What is interesting to psychologists is the widespread benefits of increasing intelligence on being able to overcome built in cognitive biases that result in errors on problems like the Wason Card Selection Task.  While this brain teaser may seem abstract and removed from everyday life, it is not.  The ‘conditional’ is a kind of logic found in lots of everyday situations – such as ‘If the person is drinking beer, then the person must be over 19 years of age’.

If your logical reasoning is faulty with these kinds of ‘rules’ you can end up reaching conclusions that are in error and which may be costly.

About the Author

Dr Mark A. Smith, is a cognitive neuroscientist and author. Between 2000 and 2003 he was a Lecturer in the Department of Experimental Psychology at the University of Cambridge.  His current research is in fluid intelligence and how training intelligence increases problem solving ability and life effectiveness. He has developed software that increases IQ and fluid intelligence that is now widely used in educational and household settings. You can find out about this software and follow his research blog on intelligence here:

HighIQPro.com

And:

HighIQPro.com/software

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