The problem below appears very simple but I can tell you this has stumped several of my classes!

What I love about this problem is that it is so accessible. Every student can give this problem a go without any hints. The less able of my groups tend to stick to the method of trial and error where asΒ more able of my groups start to think about which numbers need to be in the intersections and why. I have been using this problem (and problems like this) as extensions to my starters. My starters all tend to follow the same routine: 12 questions from mathsbot on the board followed by an extension question on my other board. I found quite early on that I have some students who will fly through the first 12 questions and I needed something to occupy them whilst the others practise the skills. I never reveal the answer to my classes until someone in the room has found the solution. This problem has genuinely been on my board now for several weeks. The other beautiful part of this is that there is more than one solution. When one of my students did finally solve this the other week they asked: is this the only solution? To which I gleefully replied ‘no, there is more than one solution’. At that reply the student quickly went about searching for a different solution.

One solution is below:

This problem and the others like it do genuinely engage my students. You could easily use it as the only starter activity or they are indeed handy to use as extension problems.

This problem and many other excellent problems are taken from the mathematical association problem pages 11- 14 book.

The price of the book is only Β£4.99 and certainly worth the investment. A link to a page to be able to purchase your own copy is here:

I hope you and your students enjoy these problems as much as my students and I do.


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