## Yesterday’s Guardian’s maths problems

Yesterday’s Guardian had some maths puzzles from Key Stage 2, 3 and GCSE level. I was pleased to note I could manage them all except number 12. At least, that’s what I thought. For example number 8. The puzzle goes like this:

Look at these diagrams:

Diagram A {1,2,3,4} 10

Diagram B {2,3,4,5} 16

Diagram C {3,4,5,6} 18

Which one is the odd one out? Explain why.

The first four numbers there are arranged clockwise around the last number. Surely the answer is that in A and C, the outside numbers add up to the middle number. So B is the odd one out. The answer given says that “There isn’t one answer for this but you must be able to justify your answer” Fair enough. But I think my answer is one of the most obvious, so why don’t they list it in the “for example…” The ones they list are the following: “A has no numbers greater than 10, the other two do; if you add the numbers on the left hand side [that’ll be the first and fourth of my lists] then double them, you should get the middle number but in B you don’t; it is only on C that two outside numbers, 3 and 6, multiply to make the middle number.” These all seem way more convoluted than my fairly elegant solution.

But it gets sillier. One of the puzzles (Number 11) doesn’t even have a solution. It is undetermined by the information given. So it’s one of those things where the numbers in the row below add up to the number in the row above. It is a triangle, three circles on the bottom, two above them and one above that. Only two entries are filled in. A little reflection will show that no two entries can determine the whole answer. Here is what the puzzle looked like, I have added letters to the empty squares to make it easy to talk about.

So the two numbers simply do not determine anything about the solution. D will have to be greater or equal to 8.2 + 5.1, A and B have to add up to 8.2 (therefore have to be less than 8.2) and C has to be at least 5.1. We are still miles from a solution. I ended up putting 8.2 in A, 0 in B. C and D were then fixed (5.1 and 13.3 respectively) But the rather arbitrary solution they give is 4.2, 4, 9.1 and 17.3 for A-D respectively. That is crazy! Where did those numbers come from?

These two questions would have bugged me loads in the exam. Maths (at school at least) is about getting THE solution. If any number of solutions are possible, isn’t this just going to trip kids up?

Incidentally, I’ve been thinking about the relationship between a sigma-algebra and a topology. Both are kinds of structure you can impose on a set X and are subsets of X’s power set. Maybe tomorrow when I’m in a LaTeX mood, I’ll write my tentative conclusions here…

## Leave a Reply