1 files changed, 69 insertions(+), 0 deletions(-)

A main.py

@@ 1,69 @@
+#!/usr/bin/env python3
+
+"""
+You and a friend are shooting some hoops at your local basketball court when
+she issues a challenge: She will name a number, which we’ll call N. Your goal
+is to score exactly N points in as many ways as possible using only 2-point
+and 3-point shots. The order of your shots does not matter.
+
+For example, there are two ways you could score N = 8 points: four 2-pointers
+or two 3-pointers and one 2-pointer.
+
+Your apparently sadistic friend chooses 60 for the value of N. You try to
+negotiate this number down, but to no avail. However, she says you are welcome
+to pick an even larger value of N. Does there exist an integer N greater than
+60 such that there are fewer ways to score N points than there are ways to
+score 60 points?
+"""
+
+def count_combinations(total_points: int) -> int:
+    counter = 0
+    for i in range(total_points // 3 + 1):
+        for j in range(total_points // 2 + 1):
+            combination = (3 * i) + (2 * j)
+            if combination == total_points:
+                counter += 1
+            elif combination > total_points:
+                break
+    return counter
+
+def test():
+    """Small test set."""
+    assert count_combinations(0) == 1 #no points
+    assert count_combinations(1) == 0 #impossible
+    assert count_combinations(2) == 1 #1 two-pointer
+    assert count_combinations(3) == 1 #1 three-pointer
+    assert count_combinations(4) == 1 #2 two-pointers and 0 three-pointers
+    assert count_combinations(5) == 1 #0 and 1
+    assert count_combinations(6) == 2 #3 and 0; 0 and 2
+    assert count_combinations(7) == 1 #1 and 2
+    assert count_combinations(8) == 2 #4 and 0; 1 and 2
+    assert count_combinations(9) == 2 #3 and 1; 0 and 3
+
+def main():
+    """Main function."""
+    sixty_points_combinations = count_combinations(60)
+    print(f"There are {sixty_points_combinations} ways to score 60 points")
+
+    n = 61
+    while True:
+        n_points_combinations = count_combinations(n)
+        if n_points_combinations < sixty_points_combinations:
+            print(f"{n} points can be scored in just {n_points_combinations} ways")
+            break
+        cursor += 1
+
+def timed_main():
+    """Main function without any printing."""
+    sixty_points_combinations = count_combinations(60)
+    n = 61
+    while True:
+        n_points_combinations = count_combinations(n)
+        if n_points_combinations < sixty_points_combinations:
+            break
+        cursor += 1
+
+if __name__ == "__main__":
+    test()
+    main()
+