diff --git a/DIRECTORY.md b/DIRECTORY.md index 18c573909..c781b17bf 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -937,6 +937,8 @@ * [Sol1](project_euler/problem_091/sol1.py) * Problem 092 * [Sol1](project_euler/problem_092/sol1.py) + * Problem 094 + * [Sol1](project_euler/problem_094/sol1.py) * Problem 097 * [Sol1](project_euler/problem_097/sol1.py) * Problem 099 diff --git a/project_euler/problem_094/__init__.py b/project_euler/problem_094/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/project_euler/problem_094/sol1.py b/project_euler/problem_094/sol1.py new file mode 100644 index 000000000..a41292fe2 --- /dev/null +++ b/project_euler/problem_094/sol1.py @@ -0,0 +1,44 @@ +""" +Project Euler Problem 94: https://projecteuler.net/problem=94 + +It is easily proved that no equilateral triangle exists with integral length sides and +integral area. However, the almost equilateral triangle 5-5-6 has an area of 12 square +units. + +We shall define an almost equilateral triangle to be a triangle for which two sides are +equal and the third differs by no more than one unit. + +Find the sum of the perimeters of all almost equilateral triangles with integral side +lengths and area and whose perimeters do not exceed one billion (1,000,000,000). +""" + + +def solution(max_perimeter: int = 10**9) -> int: + """ + Returns the sum of the perimeters of all almost equilateral triangles with integral + side lengths and area and whose perimeters do not exceed max_perimeter + + >>> solution(20) + 16 + """ + + prev_value = 1 + value = 2 + + perimeters_sum = 0 + i = 0 + perimeter = 0 + while perimeter <= max_perimeter: + perimeters_sum += perimeter + + prev_value += 2 * value + value += prev_value + + perimeter = 2 * value + 2 if i % 2 == 0 else 2 * value - 2 + i += 1 + + return perimeters_sum + + +if __name__ == "__main__": + print(f"{solution() = }")