Problem 15

Statement
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?

Solution
The code, in C.

#include <stdio.h>

long long int gridRoutes(int s){
  int i;
  long long int m=1;
  for(i=1;i<s+1;i++)
    m=(m*((s+1)*2-1-i))/i;
  return m;
}

int main(void){
  printf("%lld\n",gridRoutes(20));
}

Answer
137846528820

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