Question 84
A magic square is a square table in which the sum of the numbers in each row or column is constant. For example,
| 1 | 5 | 9 |
| :--- | :--- | :--- |
| 8 | 3 | 4 |
| 6 | 7 | 2 |
is a magic square using the numbers 1 to 9. As the reader can verify, each row or column sums to 15.
a) The square below is part of a magic square using the odd numbers from 1 to 17. Find $X$.
| | 1 | |
| :---: | :---: | :---: |
| 5 | | 13 |
| $X$ | | 3 |
b) A magic square is called hypermagic if the sum in every row, column, or diagonal is constant. Write the numbers 1 to 9 in the square below to make it hypermagic.
| 1 | 5 | 9 |
| :--- | :--- | :--- |
| 8 | 3 | 4 |
| 6 | 7 | 2 |
is a magic square using the numbers 1 to 9. As the reader can verify, each row or column sums to 15.
a) The square below is part of a magic square using the odd numbers from 1 to 17. Find $X$.
| | 1 | |
| :---: | :---: | :---: |
| 5 | | 13 |
| $X$ | | 3 |
b) A magic square is called hypermagic if the sum in every row, column, or diagonal is constant. Write the numbers 1 to 9 in the square below to make it hypermagic.