Comment by guessmyname

Lattice Paths — https://projecteuler.net/problem=15

> Starting in the top left corner of a 2x2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

   ─────────┐  ────┐       ────┐    
   ┌───┬───┐│  ┌───│───┐   ┌───│───┐
   │   │   ││  │   │   │   │   │   │
   ├───┼───┤│  ├───└────┐  ├───│───┤
   │   │   ││  │   │   ││  │   │   │
   └───┴───┘│  └───┴───┘│  └───│───┘
            ▼           ▼      └────▶
                                     
  │┌───┬───┐  │┌───┬───┐  │┌───┬───┐
  ││   │   │  ││   │   │  ││   │   │
  └─────────┐ └────┐───┤  │├───┼───┤
   │   │   ││  │   │   │  ││   │   │
   └───┴───┘│  └───│───┘  │└───┴───┘
            ▼      └────▶ └─────────▶

> How many such routes are there through a 20x20 grid?