the-honk/challenges/euler/thoughts/15 - Lattice paths.md

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### Lattice Paths

For a lattice with dimensions m x n, all paths will have m + n segments. m segments go down, n segments go right. To count m + n slots, count the ways to pick m downward moves - the rest will be rightward moves.

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<img src="https://latex.codecogs.com/svg.image?{m&space;&plus;&space;n&space;\choose&space;m}&space;=&space;{m&space;&plus;&space;n&space;\choose&space;n}&space;=&space;\frac{(m&plus;n)!}{m!n!}" height="100">

#### LaTeX

```
{m + n \choose m} = {m + n \choose n} = \frac{(m+n)!}{m!n!}
```

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