A Puzzle for You

By Michael Edmonds 28/03/2011

I came across a puzzle in a book I am reading at the moment (Flipnosis – the Art of Split Second Persuasion) by Kevin Dutton which poses the following question:


You have four cards placed in front of you. Each card bears a number or a colour on the side facing you.

Which of the cards would you need to turn over in order to test the proposition that if a card shows an even number on one side, then its opposite side is coloured red?

Apparently most people choose to turn over the red card and the number 3. However, does this really make sense? If you turn over the red card and find an odd number does this invalidate the proposition? No, it doesn’t.

Again, if you turn over the number 3 and find a red background doe this invalidate the proposition. Again, no it doesn’t.

However, if you turn over the blue card and find the number 4, for example, then you have disproven the proposition. Likewise, if you turn over the 8 and find a colour other than red, the proposition is disproven.

I like this puzzle as it shows that it can only be solved by attempting to falsify the proposition, an approach fundamental to science.

Yet, it appears that most people instinctively attempt to find conditions that conform to what we believe the “rule” to be, highlighting the problems that scientists sometimes face in trying to explain falsification and confirmation bias to non-scientists.

Perhaps such puzzles could serve as a way of explaining such terms. Food for thought.