# Count On

## Explorer

#### Magic Squares

This pattern was known in China more than 2000 years ago. It arranges the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 in a 3-by-3 square which has some remarkable properties:

6 |
1 |
8 |

7 |
5 | 3 |

2 |
9 | 4 |

What is the sum of the numbers in each row?

What about the sum of each column?

And the two diagonals?

This number is called the "magic constant" for this magic square.

We can do the same by arranging the numbers from 1 to 16 in a 4-by-4 square with a different magic constant - what is it?

16 |
3 |
2 |
13 |

5 |
10 |
11 |
8 |

9 |
6 |
7 |
12 |

4 |
15 |
14 |
1 |

- Can you...
- find a different arrangement of the numbers 1 to 9 to make a magic square with rows, columns and diagonals adding to 15 (i.e. with a magic constant of 15)?
- find a magic square of 9 numbers (not necessarily consecutive ones) where the rows, columns and diagonals add to 150?
- find a magic square of 9 numbers with a magic constant of 18?