Magic Rectangles
A magic rectangle is an m × n array of the positive integers from 1 to m × n such that the numbers in each row have a constant sum and the numbers in each column have a constant sum (although the row sum need not equal the column sum). Shown below is a 3 × 5 magic rectangle with the integers 1-15.
|
6 |
7 |
8 |
9 |
10 |
|
13 |
3 |
1 |
11 |
12 |
|
5 |
14 |
15 |
4 |
2 |
Two of three arrays above can be filled with the integers 1-24 to form a magic rectangle. Which one can’t, and why not?
This brainteaser was written by Patrick Vennebush.
