Flag-tastic
How many different flags can you make?
Age
11 to 14
Challenge level
Problem
A picture of a flag is to be completed by shading two squares that do not share an edge. The diagram shows one way in which this can be done.
Image
How many different possible completed pictures are there (including the one shown)?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 8
If the squares are numbered 1 to 6, as shown.
The possible pairings are:
1 and 4
1 and 5
1 and 6
2 and 3
2 and 5
2 and 6
3 and 6
4 and 5
If the squares are numbered 1 to 6, as shown.
| 1 |
3 |
5 |
| 2 |
4 | 6 |
The possible pairings are:
1 and 4
1 and 5
1 and 6
2 and 3
2 and 5
2 and 6
3 and 6
4 and 5