MathDB

The checker moves from the lower left corner of the board

100 \times 100

to the right top corner, moving at each step one cell to the right or one cell up. Let

a

be the number of paths in which exactly

70

steps the checker take under the diagonal going from the lower left corner to the upper right corner, and

b

is the number of paths in which such steps are exactly

110

. What is more:

a

b

Problem Statement