Problem | Teachers' Notes | Hint | Solution | Printable page |

In the following grid, how many pairs of numbers can you find that add up to a multiple of 11?

9	46	79	13
64	90	2	97
25	31	20	22
4	52	55	7

Do you notice anything interesting?

Can you find all the pairs?

Could you convince someone that you haven't missed any?

Here is another grid. This time we are interested in pairs that add up to a multiple of 13. How can you use your insights from above to find all the possible pairings?

11	54	93	15
76	106	2	115
29	37	24	26
4	62	65	9

Thank you to Susanne Mallett from Comberton Village College for introducing us to this problem.

Creating expressions/formulae. Combinations. Factors and multiples. Properties of numbers. Mathematical reasoning & proof. Visualising. Divisibility. Generalising. Workshop. Modulus arithmetic.