Change problem 121 to look cooler but make it harder to understand

python/e121.py

@@ -1,41 +1,25 @@
-from fractions import Fraction
+from math import factorial
 from itertools import combinations
 
 
-def mul(xs):
+def product(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
+    odds = [n for n in range(1, n_total + 1)]
+    return sum(map(product, combinations(odds, n_total - n_blue)))
 
 
 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
+    odds = sum([sub_odds(n_blue, n_turns)
+                for n_blue in range(n_to_win, n_turns + 1)])
+    return int(factorial(n_turns + 1) / odds)
 
 
 if __name__ == "__main__":