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TheAlgorithms · cclauss · Aug 27, 2020 · Aug 27, 2020 · Aug 27, 2020 · Aug 27, 2020
commit d55b3763e1b705f2108ae9eb73a88109e7258e35
diff --git a/project_euler/problem_63/sol1.py b/project_euler/problem_63/sol1.py
@@ -0,0 +1,31 @@
+"""
+The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number,
+134217728=89, is a ninth power.
+How many n-digit positive integers exist which are also an nth power?
+"""
+
+"""
+The maximum base can be 9 because all n-digit numbers < 10^n.
+Now 9**23 has 22 digits so the maximum power can be 22.
+Using these conclusions, we will calculate the result.
+"""
+
+
+def compute_nums(max_base: int = 10, max_power: int = 22) -> int:
+    """
+    Returns the count of all n-digit numbers which are nth power
+    >>> compute_nums(10,22)
+    49
+    """
+    bases = list(range(1, max_base))
+    powers = list(range(1, max_power))
+    count = 0
+    for base in bases:
+        for power in powers:
+            if len(str((base ** power))) == power:
+                count += 1
+    return count
+
+
+if __name__ == "__main__":
+    print(f"{compute_nums(10, 22) = }")