Copyright © University of Cambridge. All rights reserved.

## 'Elevenses' printed from http://nrich.maths.org/

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.

Click here for a poster of this problem.