Hacktoberfest: Project Euler Solution Problem 77

project_euler/problem_77/sol1.py

@@ -0,0 +1,68 @@
+"""
+Prime summations
+Problem 77
+
+It is possible to write ten as the sum of primes
+in exactly five different ways:
+
+7 + 3
+5 + 5
+5 + 3 + 2
+3 + 3 + 2 + 2
+2 + 2 + 2 + 2 + 2
+
+What is the first value which can be written
+as the sum of primes in over five thousand different ways?
+"""
+
+
+def solution(length=5000) -> int:
+    """Ways to write sum of primes
+
+    Keyword arguments:
+    amount -- amount of different ways (default 5000)
+
+    Passing no parameters returns the result
+    >>> solution()
+    71
+    """
+
+    primes = [
+        2,
+        3,
+        5,
+        7,
+        11,
+        13,
+        17,
+        19,
+        23,
+        29,
+        31,
+        37,
+        41,
+        43,
+        47,
+        53,
+        59,
+        61,
+        67,
+        71,
+        73,
+        79,
+    ]
+
+    target = 11
+    while True:
+        ways = [1] + [0] * target
+        for p in primes:
+            for i in range(p, target + 1):
+                ways[i] += ways[i - p]
+        if ways[target] > length:
+            break
+        target += 1
+    return target
+
+
+if __name__ == "__main__":
+    print(solution())