1997 PMWC Problems/Problem I15
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Problem
How many paths from A to B consist of exactly six line segments (vertical, horizontal or inclined)?
![[Asy_image]](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/1/8/4/184d51586f2fd703a8a3009cd0946974614c58b1.png "Click to view code")
Solution
- Ignoring the diagonal segments, there are
paths.
- Traversing the diagonals, we quickly find that the path must run through exactly 2 diagonals. There are
pairs of diagonals through which this is possible; quick counting shows us that each pair of diagonals yields 2 paths. So there are 6 more cases here.
In total, we get 
paths.
See also
| 1997 PMWC (Problems) | ||
| Preceded by Problem I14 | Followed by Problem T1 | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
