Problem 045

git-svn-id: file:///srv/svn/euler@71 e5f4c3ec-3c0c-11df-b522-21efaa4426b5

e045.py

@@ -0,0 +1,54 @@
+"""After 40755, what is the next triangle number that is also pentagonal and hexagonal?
+
+Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
+
+Triangle    Tn=n(n+1)/2    1, 3, 6, 10, 15, ...
+Pentagonal  Pn=n(3n-1)/2    1, 5, 12, 22, 35, ...
+Hexagonal   Hn=n(2n-1)      1, 6, 15, 28, 45, ...
+
+It can be verified that T285 = P165 = H143 = 40755.
+
+Find the next triangle number that is also pentagonal and hexagonal.
+"""
+
+def triangle_generator(start = 0):
+    n = start
+    while True:
+        n = n + 1
+        yield n * (n + 1) / 2
+def pentagonal_generator(start = 0):
+    n = start
+    while True:
+        n = n + 1
+        yield n * (3 * n - 1) / 2
+def hexagonal_generator(start = 0):
+    n = start
+    while True:
+        n = n + 1
+        yield n * (2 * n - 1)
+
+MIN = 40755
+
+def main():
+    pent_count = 0
+    tri_count = 0
+    for hex in hexagonal_generator():
+        if hex <= MIN:
+            continue
+        # Catch up the other generators
+        for pent in pentagonal_generator(pent_count):
+            pent_count = pent_count + 1
+            if pent >= hex:
+                break
+        if pent > hex:
+            continue
+        for tri in triangle_generator(tri_count):
+            tri_count = tri_count + 1
+            if tri >= hex:
+                break
+        if tri > hex:
+            continue
+        print 'Next number is:', hex
+        break
+if __name__ == '__main__':
+    main()