Project Euler

Problem 15: Lattice paths

Starting in the top left corner of a 2×2 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 20×20 grid? Run this solution at repl.io here.

      
        #So solution does not require code: it is simply 2n Choose n:
        # 40 choose 20 = 137846528820

        def factorial(n):
          result = 1

          for n in range(2,n+1):
            result = result * n
          
          return result
          
        def countpath(n):
          #counting over a square grid from corner to corner
          
          combination = factorial(2*n) // (factorial(n) * factorial(n))
          
          return(combination)

        print(countpath(20))
      
    

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