What is the maximum number of regions into which 8 chords can divide a circle?
Solution:
The answer is 37 regions.
The maximum number of regions is achieved by using chords which are not not parallel, not concurrent, and not intersecting on the circle. Look at a table:
Number of chords |
Number of regions |
1 | 2 |
2 | 4 |
3 | 7 |
4 | 11 |
5 | 16 |
6 | 22 |
... | ... |
n | (n^2 + n + 2) / 2 |
So, for 8 chords,
(64 + 8 + 2) / 2 = 74 / 2 = 37
Correctly solved by:
1. Kelley Britz | Winchester, VA |
2. Jeremy Ramsey | Winchester, VA |
3. Trey Genda | Winchester, VA |
4. Krista Ramey | Winchester, VA |