From 806734c6f92ad92736e1ff168f2217e2318e3336 Mon Sep 17 00:00:00 2001
From: Freddy Pringle <freddyjepringle@gmail.com>
Date: Mon, 7 Dec 2020 18:20:03 +0100
Subject: [PATCH 1/3] Added solution for Project Euler problem 121

---
 project_euler/problem_121/__init__.py |  0
 project_euler/problem_121/sol1.py     | 65 +++++++++++++++++++++++++++
 2 files changed, 65 insertions(+)
 create mode 100644 project_euler/problem_121/__init__.py
 create mode 100644 project_euler/problem_121/sol1.py

diff --git a/project_euler/problem_121/__init__.py b/project_euler/problem_121/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/project_euler/problem_121/sol1.py b/project_euler/problem_121/sol1.py
new file mode 100644
index 000000000000..11a8eb71544b
--- /dev/null
+++ b/project_euler/problem_121/sol1.py
@@ -0,0 +1,65 @@
+"""
+A bag contains one red disc and one blue disc. In a game of chance a player takes a
+disc at random and its colour is noted. After each turn the disc is returned to the
+bag, an extra red disc is added, and another disc is taken at random.
+
+The player pays £1 to play and wins if they have taken more blue discs than red
+discs at the end of the game.
+
+If the game is played for four turns, the probability of a player winning is exactly
+11/120, and so the maximum prize fund the banker should allocate for winning in this
+game would be £10 before they would expect to incur a loss. Note that any payout will
+be a whole number of pounds and also includes the original £1 paid to play the game,
+so in the example given the player actually wins £9.
+
+Find the maximum prize fund that should be allocated to a single game in which
+fifteen turns are played.
+
+
+Solution:
+    For each 15-disc sequence of red and blue for which there are more red than blue,
+    we calculate the probability of that sequence and add it to the total probability
+    of the player winning. The inverse of this probability gives an upper bound for
+    the prize if the banker wants to avoid an expected loss.
+"""
+
+from itertools import product
+from typing import Tuple
+
+
+def solution(num_turns: int = 15) -> int:
+    """
+    Find the maximum prize fund that should be allocated to a single game in which
+    fifteen turns are played.
+    >>> solution(4)
+    10
+    >>> solution(10)
+    225
+    """
+    total_prob: float = 0.0
+    prob: float
+    num_blue: int
+    num_red: int
+    ind: int
+    col: int
+    series: Tuple[int, ...]
+
+    for series in product(range(2), repeat=num_turns):
+        num_blue = series.count(1)
+        num_red = num_turns - num_blue
+        if num_red >= num_blue:
+            continue
+        prob = 1.0
+        for ind, col in enumerate(series, 2):
+            if col == 0:
+                prob *= (ind - 1) / ind
+            else:
+                prob *= 1 / ind
+
+        total_prob += prob
+
+    return int(1 / total_prob)
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")

From 9a70a3ff1ee0c285d8d7ccfb4a12399b563d9b29 Mon Sep 17 00:00:00 2001
From: Freddy Pringle <freddyjepringle@gmail.com>
Date: Sat, 6 Mar 2021 16:03:53 +0100
Subject: [PATCH 2/3] Updated typing for 3.9

---
 project_euler/problem_121/sol1.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/project_euler/problem_121/sol1.py b/project_euler/problem_121/sol1.py
index 11a8eb71544b..93679cf4a897 100644
--- a/project_euler/problem_121/sol1.py
+++ b/project_euler/problem_121/sol1.py
@@ -24,7 +24,6 @@
 """
 
 from itertools import product
-from typing import Tuple
 
 
 def solution(num_turns: int = 15) -> int:
@@ -42,7 +41,7 @@ def solution(num_turns: int = 15) -> int:
     num_red: int
     ind: int
     col: int
-    series: Tuple[int, ...]
+    series: tuple[int, ...]
 
     for series in product(range(2), repeat=num_turns):
         num_blue = series.count(1)

From 9dbcdaea233f54c83e815abcb61b806f843895b2 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Sat, 6 Mar 2021 15:20:45 +0000
Subject: [PATCH 3/3] updating DIRECTORY.md

---
 DIRECTORY.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index dfb673dea829..040001f0c7dd 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -771,6 +771,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_119/sol1.py)
   * Problem 120
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_120/sol1.py)
+  * Problem 121
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_121/sol1.py)
   * Problem 123
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_123/sol1.py)
   * Problem 125