MathDB

A robot is standing on the bottom left vertex

(0,0)

of a

5\times5

grid, and wants to go to

(5,5)

, only moving to the right

(a,b)\mapsto(a+1,b)

or upward

(a,b)\mapsto(a,b+1)

. However this robot is not programmed perfectly, and sometimes takes the upper-left diagonal path

(a,b)\mapsto(a-1,b+1)

. As the grid is surrounded by walls, the robot cannot go outside the region

0\leq a,b\leq5

. Supposing that the robot takes the diagonal path exactly once, compute the number of different routes the robot can take.

Problem Statement