feat(euler): 30 - digit fifth powers

challenges/euler/readme.md

@@ -41,7 +41,7 @@ The source code can be found in the [src](src) directory. My thoughts about some
 -   [ ] 27 - Quadratic primes
 -   [x] [28 - Number spiral diagonals](src/28%20-%20Number%20spiral%20diagonals.ts)
 -   [ ] 29 - Distinct powers
--   [ ] 30 - Digit fifth powers
+-   [x] [30 - Digit fifth powers](src/30%20-%20Digit%20fifth%20powers.ts)
 -   [ ] 31 - Coin sums
 -   [ ] 32 - Pandigital products
 -   [ ] 33 - Digit cancelling fractions

challenges/euler/src/30 - Digit fifth powers.ts

@@ -0,0 +1,38 @@
+// Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
+// 1634 = 1^4 + 6^4 + 3^4 + 4^4
+// 8208 = 8^4 + 2^4 + 0^4 + 8^4
+// 9474 = 9^4 + 4^4 + 7^4 + 4^4
+// As 1 = 1^4 is not a sum it is not included.
+// The sum of these numbers is 1634 + 8208 + 9474 = 19316.
+// Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
+export = {};
+
+// something times 9^5 = x digit number
+// 9^5 = 59049 therefore x >= 5
+// 6 * 9^5 = 354294
+
+const powers = [];
+
+for (let i = 0; i < 10; i++) {
+    powers.push(i ** 5);
+}
+
+const powerSum = (n: number) => {
+    let sum = 0;
+
+    while (n > 0) {
+        sum += powers[n % 10];
+        n = (n / 10) | 0;
+    }
+
+    return sum;
+};
+
+let sum = 0;
+
+for (let i = 10; i < 6 * powers[9]; i++) {
+    if (i === powerSum(i)) sum += i;
+}
+
+// Output
+console.log(sum);