A nice How many ways to pick the fruit puzzle reminded me about a similar puzzle, with quite different solution.
Let's say Alice and Bob quarrelled and decided to split up their field. Now Alice can run her machine only in the upper part of the field and can never go below the main diagonal. See example on the picture. In how many ways could she make the one trip from the top-left square to her home?
In other words, what is the number of paths on NxN grid, which go strictly to the right or down, start from the top-left, end to the bottom-right square and never cross the diagonal?
P.S. I'm replacing 20x20 by NxN in order to avoid numerical solutions, which are quite straight forward of course.