From df525339136fa9f7a1b237c76f7d12ef462c4181 Mon Sep 17 00:00:00 2001
From: newt <hi@newty.dev>
Date: Wed, 9 Oct 2024 18:02:36 +0100
Subject: [PATCH] (euler): #12

---
 ...12 - Highly Divisible Triangular Number.ts | 39 +++++++++++++++++++
 euler/tsconfig.json                           |  3 +-
 2 files changed, 41 insertions(+), 1 deletion(-)
 create mode 100644 euler/src/12 - Highly Divisible Triangular Number.ts

diff --git a/euler/src/12 - Highly Divisible Triangular Number.ts b/euler/src/12 - Highly Divisible Triangular Number.ts
new file mode 100644
index 0000000..91f6f1f
--- /dev/null
+++ b/euler/src/12 - Highly Divisible Triangular Number.ts	
@@ -0,0 +1,39 @@
+export {};
+
+const factorsOf = (num: number) => {
+    const isEven = num % 2 === 0;
+    const max = Math.sqrt(num);
+    const inc = isEven ? 1 : 2;
+    const factors = [1, num];
+
+    for (let curFactor = isEven ? 2 : 3; curFactor <= max; curFactor += inc) {
+        if (num % curFactor !== 0) continue;
+        factors.push(curFactor);
+
+        let compliment = num / curFactor;
+        if (compliment !== curFactor) factors.push(compliment);
+    }
+
+    return factors;
+};
+
+// https://www.mathsisfun.com/algebra/triangular-numbers.html
+const nthTriangleNumber = (n: number) => (n * (n + 1)) / 2;
+
+const firstTriangleWithOverNDivisors = (n: number) => {
+    let divisorCountFound = false;
+    let i = 1;
+
+    while (!divisorCountFound) {
+        const triangle = nthTriangleNumber(i);
+        const factors = [...factorsOf(triangle)];
+        i++;
+
+        if (factors.length > n) {
+            divisorCountFound = true;
+            return triangle;
+        }
+    }
+};
+
+console.log(firstTriangleWithOverNDivisors(500));
diff --git a/euler/tsconfig.json b/euler/tsconfig.json
index 4f16804..7345e25 100644
--- a/euler/tsconfig.json
+++ b/euler/tsconfig.json
@@ -2,7 +2,8 @@
     "compilerOptions": {
         "target": "es5",
         "module": "commonjs",
-        "outDir": "build"
+        "outDir": "build",
+        "downlevelIteration": true
     },
     "include": ["src/**/*.ts"],
     "exclude": ["node_modules"]