From 9701e459e884e883fc720277452ec592eae305d0 Mon Sep 17 00:00:00 2001
From: Maxim Smolskiy <mithridatus@mail.ru>
Date: Tue, 14 Mar 2023 08:39:36 +0300
Subject: [PATCH] Add Project Euler problem 100 solution 1 (#8175)

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 DIRECTORY.md                          |  2 ++
 project_euler/problem_100/__init__.py |  0
 project_euler/problem_100/sol1.py     | 48 +++++++++++++++++++++++++++
 3 files changed, 50 insertions(+)
 create mode 100644 project_euler/problem_100/__init__.py
 create mode 100644 project_euler/problem_100/sol1.py

diff --git a/DIRECTORY.md b/DIRECTORY.md
index b2daaaa9c..e1ce44eed 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -937,6 +937,8 @@
     * [Sol1](project_euler/problem_097/sol1.py)
   * Problem 099
     * [Sol1](project_euler/problem_099/sol1.py)
+  * Problem 100
+    * [Sol1](project_euler/problem_100/sol1.py)
   * Problem 101
     * [Sol1](project_euler/problem_101/sol1.py)
   * Problem 102
diff --git a/project_euler/problem_100/__init__.py b/project_euler/problem_100/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/project_euler/problem_100/sol1.py b/project_euler/problem_100/sol1.py
new file mode 100644
index 000000000..367378e7a
--- /dev/null
+++ b/project_euler/problem_100/sol1.py
@@ -0,0 +1,48 @@
+"""
+Project Euler Problem 100: https://projecteuler.net/problem=100
+
+If a box contains twenty-one coloured discs, composed of fifteen blue discs and
+six red discs, and two discs were taken at random, it can be seen that
+the probability of taking two blue discs, P(BB) = (15/21) x (14/20) = 1/2.
+
+The next such arrangement, for which there is exactly 50% chance of taking two blue
+discs at random, is a box containing eighty-five blue discs and thirty-five red discs.
+
+By finding the first arrangement to contain over 10^12 = 1,000,000,000,000 discs
+in total, determine the number of blue discs that the box would contain.
+"""
+
+
+def solution(min_total: int = 10**12) -> int:
+    """
+    Returns the number of blue discs for the first arrangement to contain
+    over min_total discs in total
+
+    >>> solution(2)
+    3
+
+    >>> solution(4)
+    15
+
+    >>> solution(21)
+    85
+    """
+
+    prev_numerator = 1
+    prev_denominator = 0
+
+    numerator = 1
+    denominator = 1
+
+    while numerator <= 2 * min_total - 1:
+        prev_numerator += 2 * numerator
+        numerator += 2 * prev_numerator
+
+        prev_denominator += 2 * denominator
+        denominator += 2 * prev_denominator
+
+    return (denominator + 1) // 2
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")