no of ways to move on a 2x6 grid
Source: Chile Finals 2006 L2 p3
October 3, 2022
combinatorics
Problem Statement
We have the following board of .
[asy]
unitsize(0.8 cm);int i;draw((0,0)--(6,0));
draw((0,1)--(6,1));
draw((0,2)--(6,2));for (i = 0; i <= 6; ++i) {
draw((i,0)--(i,2));
}dot("", (0,2), NW);
dot("", (6,2), NE);
dot("", (3,0), S);
[/asy]
Find in how many ways you can go from point to point , moving by the segments of the board, respecting the following rules:
- You cannot pass through the same point twice.
- You can only make three types of movements moving through the segments: To the right, up, down
- You have to go through point .