Solve problem 121 in Python and update template creation lib

python/e121.py

@@ -0,0 +1,45 @@
+from fractions import Fraction
+from itertools import combinations
+
+
+def mul(xs):
+    r = 1
+    for x in xs:
+        r *= x
+    return r
+
+
+def mul_inv(xs):
+    r = 1
+    for x in xs:
+        r *= (1 - x)
+    return r
+
+
+def sub_odds(n_blue, n_total):
+    """ Computes the odds for getting exactly n_blue out of n_total blue discs.
+    """
+    total_odds = 0
+    odds = [Fraction(1, n) for n in range(2, 2 + n_total)]
+    odds_set = set(odds)
+    for odd in combinations(odds, n_blue):
+        odd_inv = tuple(odds_set.difference(set(odd)))
+        total_odds += mul(odd) * mul_inv(odd_inv)
+    return total_odds
+
+
+def euler_121():
+    n_turns = 15
+    n_to_win = n_turns // 2 + 1
+    odds = 0
+    for n_blue in range(n_to_win, n_turns + 1):
+        odds += sub_odds(n_blue, n_turns)
+    price = int(1 / odds)
+    return price
+
+
+if __name__ == "__main__":
+    solution = euler_121()
+    print("e121.py: " + str(solution))
+    assert(solution == 2269)
+