MathDB

3

Part of 2006 Chile National Olympiad

Problems(1)

no of ways to move on a 2x6 grid

Source: Chile Finals 2006 L2 p3

10/3/2022
We have the following board of 2×62 \times 6. [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("AA", (0,2), NW); dot("BB", (6,2), NE); dot("CC", (3,0), S); [/asy] Find in how many ways you can go from point AA to point BB, 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 CC.
combinatorics