diff --git a/Project-Euler/Problem001.js b/Project-Euler/Problem001.js
index c47c10bd1c..a88f912603 100644
--- a/Project-Euler/Problem001.js
+++ b/Project-Euler/Problem001.js
@@ -1,20 +1,23 @@
// https://projecteuler.net/problem=1
-/* Multiples of 3 and 5
- If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
+/* Multiples of 3 and 5
+If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6, and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below the provided parameter value number.
*/
+// This method uses the nSum function to add the nSum for 3 and 5. However, it needs to subtract the nSum for 15 once to avoid double counting.
const multiplesThreeAndFive = (num) => {
if (num < 1) throw new Error('No natural numbers exist below 1')
+ num -= 1
+ let sum = 0
- let total = 0
- // total for calculating the sum
- for (let i = 1; i < num; i++) {
- if (i % 3 === 0 || i % 5 === 0) {
- total += i
- }
- }
- return total
+ // The nSum function calculates the sum of the first n numbers in the sequence with a common difference of num.
+ // Here, n is denoted as frequency.
+ const nSum = (num, frequency) => (frequency * (frequency + 1) * num) >> 1
+
+ sum += nSum(3, Math.floor(num / 3))
+ sum += nSum(5, Math.floor(num / 5))
+ sum -= nSum(15, Math.floor(num / 15))
+ return sum
}
export { multiplesThreeAndFive }
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