Illuminations: Magic Rectangles
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.
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Resource k12
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.
Problem and solution
What are you looking for?
Organization
Website URL
Type of Resource
PDF File