Home > Maths, Pedagogy, Teaching > The Importance of Diagrams – Chessboard Puzzle

## The Importance of Diagrams – Chessboard Puzzle

Have you “liked” brilliant.org on Facebook yet? Have you downloaded the app? If not, you should, it’s hours of fun. The Facebook page posts a stream of puzzles and problems to get you thinking, most can be solved mentally and serve as a nice exercise when you have a few spare minutes. A lot of them are a little less obvious than they appear!

This one is one I enjoyed:

The numbers 1-64 are written in order on a chessboard, what is the yellow sum subtract the white sum?

Fun, isn’t it? Have you got an answer? Good.

At first I thought, duh, it’s clearly 32, the yellows are all one more than the whites, but then I noticed that 64 fell on a white square. I realised I’d made a false assumption! An easy trap to fall into, the colouring of the chessboard is such that the end of one line and the beginning of tge next are the same colour, leading to a situation where every other line it is the white that is 1 greater than the yellow, leading to an answer of 0.

I like this as it serves as an excellent example of why a sketch or diagram can make something a lot clearer, and I may try it out on my sixth formers to see if they fall into the trao and try to hit home the message about diagrams. I’ve still got some who need constant reminders to sketch mechanics and graph problems!

Categories: Maths, Pedagogy, Teaching
1. February 8, 2015 at 11:28 pm

I love this and I genuinely believe that regular puzzles help to create and maintain high level functioning.

1. November 15, 2015 at 5:25 pm
2. December 10, 2015 at 11:16 pm
3. December 10, 2015 at 11:17 pm