A friend of mine has set me the challenge of finding an example of the following:
Is there a question, that everyone (both mathematicians and non-mathematicians) can understand, that most mathematicians would answer correctly, instantly, but that most non-mathematician would struggle to solve/take longer to arrive at a solution?
When I say mathematician, I mean a person who has studied maths at degree level. The key feature of such a question is that it should be understandable to an average person. I realise, of course, that this is a subjective question – what does ‘most mathematicians’ mean, what would ‘most mathematicians’ be able to answer? Nonetheless, I would be interested to hear peoples’ opinions and ideas:
Can you think of a question, that in your opinion, is an example of the above?
An example of such a question, I think, would provide a good way of explaining to people how mathematicians think. It could also be a good teaching tool (i.e to show how mathematicians approach problem solving).
My friend suggested the following question:
Does there exist a completed Sudoku grid with top row 1,2,3,4,5,6,7,8,9?
I won’t give the answer (so that you can see for yourself if it works!). When we asked this to fellow maths researchers, nearly all were able to give the correct answer immediately. When I asked the undergraduates that I teach, most of them (but not all) could answer correctly and pretty quickly. I like this question but I’m sure there’s a better one.
Edit: As for the Sudoku question, most of the researchers I asked answered in 10 seconds with the solution:
Yes. You can relabel any Sudoku (i.e swaps sets of numbers – change all 1s for 2s for example) and still have a valid Sudoku solution. So, in a sense all Sudoku are equivalent to a Sudoku with one to nine in the first row.
The standard test for distinguishing mathematicians from normal people is a two-part test. In Part One, there is a kettle full of water on the floor, and a stove with one burner lit: how do you heat the water in the kettle? Everyone answers, pick the kettle up off the floor, and put it on the lit burner.
In Part Two, there is a kettle of water on a table, and a stove with one burner lit: how do you heat the water in the kettle? If you answered, take the kettle off the table, and put it on the lit burner, well, there’s nothing wrong with that answer, but it does prove you’re not a mathematician. The mathematician’s answer is,
take the kettle off the table, and put it on the floor. This reduces it to a problem already solved.