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# Let's Face It

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### Consecutive Numbers

### Exploring Wild & Wonderful Number Patterns

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Age 7 to 11

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In this problem, you will probably find it helps to do the solution practically. A good way to do this is to draw the net of a cube and to mark a $4$ by $4$ square on each face. Then fill in the numbers for the magic square on one face.

1 | 8 | 12 | 13 |

15 | 10 | 6 | 3 |

14 | 11 | 7 | 2 |

4 | 5 | 9 | 16 |

After that you need to work your way over the net, putting a variation of the magic square on each face, and making the numbers coming on the edges of the cube correspond. Then you can make your net into a cube. We'll leave that to you!

This solution to the problem was sent in by Joel of ACS Independent, Singapore.

Here you have the net of a cube with a magic square on each face.

13 |
2 |
3 |
16 |
||||||||

11 |
8 |
5 |
10 |
||||||||

6 |
9 |
12 |
7 |
||||||||

4 |
15 |
14 |
1 |
||||||||

13 |
11 |
6 |
4 |
4 |
15 |
14 |
1 |
1 |
7 |
10 |
16 |

8 |
2 |
15 |
9 |
9 |
6 |
7 |
12 |
12 |
14 |
3 |
5 |

12 |
14 |
3 |
5 |
5 |
10 |
11 |
8 |
8 |
2 |
15 |
9 |

1 |
7 |
10 |
16 |
16 |
3 |
2 |
13 |
13 |
11 |
6 |
4 |

16 |
3 |
2 |
13 |
||||||||

10 |
5 |
8 |
11 |
||||||||

7 |
12 |
9 |
6 |
||||||||

1 |
14 |
15 |
4 |
||||||||

1 |
14 |
15 |
4 |
||||||||

12 |
7 |
6 |
9 |
||||||||

8 |
11 |
10 |
5 |
||||||||

13 |
2 |
3 |
16 |

These two group activities use mathematical reasoning - one is numerical, one geometric.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.