Starting in the top left corner of a 2*2 grid, there are 6 routes (without backtracking) to the bottom right corner.How many routes are there through a 20*20 grid?
This is not a particular question for programming ,it seems like a more mathematics problem for me . for moving from top left to right down , only consist two direction "down/ right", all path is a combination of 20 down and 20 right moves, so ,solution is just number of combination 20 of 40 instruction on move .
For Calculation,just using R:
Solution is : 137846528820