From 7faa1687616c4a52af4af7d6914db9e163b2c593 Mon Sep 17 00:00:00 2001
From: gikf <60067306+gikf@users.noreply.github.com>
Date: Mon, 24 May 2021 19:43:58 +0200
Subject: [PATCH] fix(curriculum): rework Project Euler 85 (#42181)

* fix: rework challenge to use argument in function

* fix: add solution

* fix: grammar
---
 .../problem-85-counting-rectangles.md         | 77 +++++++++++++++++--
 1 file changed, 69 insertions(+), 8 deletions(-)

diff --git a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-85-counting-rectangles.md b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-85-counting-rectangles.md
index 527ddd1ab7..5db9e13fec 100644
--- a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-85-counting-rectangles.md
+++ b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-85-counting-rectangles.md
@@ -12,20 +12,44 @@ By counting carefully it can be seen that a rectangular grid measuring 3 by 2 co
 
 <img class="img-responsive center-block" alt="a diagram of the different rectangles found within a 3 by 2 rectangular grid" src="https://cdn-media-1.freecodecamp.org/project-euler/counting-rectangles.png" style="background-color: white; padding: 10px;">
 
-Although there exists no rectangular grid that contains exactly two million rectangles, find the area of the grid with the nearest solution.
+Although there may not exists a rectangular grid that contains exactly `n` rectangles, find the area of the grid with the nearest solution.
 
 # --hints--
 
-`countingRectangles()` should return a number.
+`countingRectangles(18)` should return a number.
 
 ```js
-assert(typeof countingRectangles() === 'number');
+assert(typeof countingRectangles(18) === 'number');
 ```
 
-`countingRectangles()` should return 2772.
+`countingRectangles(18)` should return `6`.
 
 ```js
-assert.strictEqual(countingRectangles(), 2772);
+assert.strictEqual(countingRectangles(18), 6);
+```
+
+`countingRectangles(250)` should return `22`.
+
+```js
+assert.strictEqual(countingRectangles(250), 22);
+```
+
+`countingRectangles(50000)` should return `364`.
+
+```js
+assert.strictEqual(countingRectangles(50000), 364);
+```
+
+`countingRectangles(1000000)` should return `1632`.
+
+```js
+assert.strictEqual(countingRectangles(1000000), 1632);
+```
+
+`countingRectangles(2000000)` should return `2772`.
+
+```js
+assert.strictEqual(countingRectangles(2000000), 2772);
 ```
 
 # --seed--
@@ -33,16 +57,53 @@ assert.strictEqual(countingRectangles(), 2772);
 ## --seed-contents--
 
 ```js
-function countingRectangles() {
+function countingRectangles(n) {
 
   return true;
 }
 
-countingRectangles();
+countingRectangles(18);
 ```
 
 # --solutions--
 
 ```js
-// solution required
+function countingRectangles(n) {
+  function numberOfRectangles(h, w) {
+    return (h * (h + 1) * w * (w + 1)) / 4;
+  }
+
+  function rectangleArea(h, w) {
+    return h * w;
+  }
+
+  let rectanglesCount = 1;
+  let maxSide = 1;
+  while (rectanglesCount < n) {
+    maxSide++;
+    rectanglesCount = numberOfRectangles(maxSide, 1);
+  }
+
+  let bestDiff = Math.abs(rectanglesCount - n);
+  let bestSize = [maxSide, 1];
+
+  let curHeight = maxSide - 1;
+  let curWidth = 1;
+
+  for (curWidth; curWidth < curHeight; curWidth++) {
+    for (curHeight; curHeight > curWidth; curHeight--) {
+      rectanglesCount = numberOfRectangles(curHeight, curWidth);
+      const curDiff = Math.abs(rectanglesCount - n);
+      if (curDiff < bestDiff) {
+        bestDiff = curDiff;
+        bestSize = [curHeight, curWidth];
+      }
+
+      if (rectanglesCount < n) {
+        break;
+      }
+    }
+  }
+  return rectangleArea(...bestSize);
+}
 ```