Square Routes


If you fit Pascal’s triangle into a grid, then each cell displays the number of distinct paths that lead to that cell from the upper left (assuming only rightward and downward movements and no backtracking).

So, above, the cell marked 4 in the second row, fourth column, can be reached in 4 ways: 1-1-1-4, 1-1-3-4, 1-2-3-4, and 1-2-3-4.