Solve problem 162.

python/e162.py

@@ -0,0 +1,39 @@
+from functools import lru_cache
+
+
+@lru_cache
+def combs(xs, first=False):
+    if xs == (0, 0, 0, 0):
+        return 1
+    
+    c = 0
+    z, o, a, r = xs
+
+    if (not first) and z > 0:
+        c += combs((z - 1, o, a, r))
+    if o > 0:
+        c += combs((z, o - 1, a, r))
+    if a > 0:
+        c += combs((z, o, a - 1, r))
+    if r > 0:
+        c += 13 * combs((z, o, a, r - 1))
+    return c
+
+
+def euler_162():
+    t = 0
+    for n in range(17):
+        for z in range(1, n + 1):
+            for o in range(1, n + 1):
+                for a in range(1, n + 1):
+                    r = n - z - o - a
+                    if not r >= 0:
+                        continue
+                    t += combs((z, o, a, r), True)
+    return hex(t)[2:].upper()
+
+
+if __name__ == "__main__":
+    solution = euler_162()
+    print("e162.py: " + str(solution))
+    assert(solution == "3D58725572C62302")