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Problem 15: Lattice Paths

Starting in the top left corner of a $2 \times 2$ grid, and only being able to move to the right and down, there are exactly $6$ routes to the bottom right corner.

How many such routes are there through a $20 \times 20$ grid?

Expected Output

Published: Friday, 19th April 2002, 12:00 pm
Difficulty rating: 5%
Overview (PDF): problem 15
Forum problem: problem 15