White Dot, Black Dot
Discrete Mathematics
Level
4
The diagram below shows a \(2 \times 10\) grid of dots (of negligible size) that alternate between black and white. How many ways are there to draw ten line segments between the dots such that
- each white dot is connected to exactly one black dot (and vice versa),
- no segment passes through more than two dots, and
- none of the segments intersect each other?
Bonus: Generalize for drawing \(n\) segments on a \(2 \times n\) grid, where \(n\) is a positive integer.
by
Steven Yuan