Project Euler #912: Where are the Odds?

I don't remember the problem number or its title, but it involved starting from the top-left corner of a 2D grid and finding how many possible paths there are to get to the bottom-right corner while only moving either down or right.

My naive solution was a brute-force depth-first recursive search. On my CPU at the time, it took about 3 minutes to solve. I thought, the logic of this is incredibly simple, why not do it in assembly?

My assembly solution took 5 minutes.

I decompiled the compiled C code to see what it had done, but I couldn't understand it. My assembly knowledge was too basic.

Thinking on it now, I wonder if a modern compiler would solve the entire problem at compile-time and just hard-code the answer to be output at runtime.

> 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.

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