# Did you solve it? The logic question almost everyone gets wrong

The results are in and yes, most of you got this one wrong. Heres why.

Earlier today I set you this puzzle:

Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

• A: Yes
• B: No
• C: Cannot be determined

Before I get to the explanation, a few words on why I set the question. I wanted to test if it really was the case that more than 80 per cent of people choose C. Well, the results are in, and with more than 200,000 submissions, this is how you voted:

• A 27.68 per cent
• B 4.55 per cent
• C 67.77 per cent

More than 72 per cent of you chose the wrong answer. Maybe its an exaggeration to say that almost everyone gets this question wrong but the vast majority of you did! (And thats not accounting for the fact that many of you who took part are seasoned readers of this puzzle column, and were warned that this question was not all it seemed.)

Why is this question so tricky? It is because it appears to give you insufficient information. Annes marital status is not known, nor can it be determined, and so you make the inference that the question posed cannot be determined.

In fact, Annes marital status is irrelevant to the answer. If she is married, then a married person is looking at an unmarried person (Anne is looking at George), and if she isnt, a married person is looking at an unmarried person (Jack is looking at Anne).

Written down it becomes more obvious. If > means looking at then:

Jack > Anne > George, or

Married > Unknown > Unmarried

Replace Unkown with Married or with Unmarried and either way there is clearly a married person looking at an unmarried one.

The puzzle caused many hands to be slapped on many foreheads.

As I expected, some people blamed getting the answer wrong on the poor wording of the question. For those of you who thought that Anne was not a person, then yes, C is the correct answer. But, come on guys, we can assume that Anne is a human being.

Others said that married and unmarried are not binary states, since what about widowed, or divorced. The Wikipedia article on marital status clears that one up.

Todays puzzle really belongs more to psychology than it does to mathematics or logic, as it is about the lazy assumptions we make, rather than whether or not we have the ability to solve the question.

Yet the reasoning that is used – that in order to solve something we need to consider all possibilities without knowing which is true – is frequently used in maths. In this video, the brilliant James Grime gives an example using irrational numbers.

Source of todays puzzle: Rational and Irrational Thought: The Thinking That IQ Tests Miss by Keith E Stanovich, Scientific American.

I post a puzzle here every second Monday. My most recent book is Snowflake Seashell Star, a colouring book of mathematical images for all ages. (In the US its title is Patterns of the Universe.)

You can check me out on Twitter, Facebook, Google+ and my personal website. And if know of any great puzzles that you would like me to set here, get in touch.