MathDB

Gus is an inhabitant on an

11

11

grid of squares. He can walk from one square to an adjacent square (vertically or horizontally) in

1

unit of time. There are also two vents on the grid, one at the top left and one at the bottom right. If Gus is at one vent, he can teleport to the other vent in

0.5

units of time. Let an ordered pair of squares

(a,b)

on the grid be sus if the fastest path from

a

b

requires Gus to teleport between vents. Walking on top of a vent does not count as teleporting between vents. What is the total number of ordered pairs of squares that are sus? Note that the pairs

(a_1,b_1)

and

(a_2,b_2)

are considered distinct if and only if

a_1 \ne a_2

b_1 \ne b_2

Problem Statement