MathDB

Let m and n be positive integers. Alice wishes to walk from the point

(0, 0)

to the point

(m,n)

in increments of

(1, 0)

and

(0, 1)

, and Bob wishes to walk from the point

(0,1)

to the point

(m, n + 1)

in increments of

(1, 0)

and

(0,1)

. Find (with proof) the number of ways for Alice and Bob to get to their destinations if their paths never pass through the same point (even at different times).

Problem Statement