Solved problem 15

0015-number-of-path-20-20.py

@@ -0,0 +1,23 @@
+"""
+Problem 15
+
+Starting in the top left corner of a 2x2 grid, there are 6 routes (without backtracking) to the bottom right corner.
+
+How many routes are there through a 20x20 grid?
+"""
+def pascals_triangle(n):
+    x=[[1]]
+    for i in range(n-1):
+        x.append([sum(i) for i in zip([0]+x[-1],x[-1]+[0])])
+    return x
+
+def solve():
+    # It turns out that the number of paths follow the pattern as
+    # The middle number of pascal triangle in the odd numbered rows
+    # For a 20x20 grid
+    rows = 20
+    columns = 20
+    triangle = pascals_triangle(2*rows + 1)
+    return triangle[2*rows][columns]
+
+print "Answer by traditional method:", solve()