From 8ac8772da1ec72537451e69a360ac7e941c836bc Mon Sep 17 00:00:00 2001
From: gikf <60067306+gikf@users.noreply.github.com>
Date: Wed, 26 May 2021 10:52:42 +0200
Subject: [PATCH] fix(curriculum): rework Project Euler 86 (#42189)

* fix: rework challenge to use argument in function

* fix: add solution
---
 .../project-euler/problem-86-cuboid-route.md  | 60 ++++++++++++++++---
 1 file changed, 51 insertions(+), 9 deletions(-)

diff --git a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-86-cuboid-route.md b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-86-cuboid-route.md
index 358806c952..caa496a114 100644
--- a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-86-cuboid-route.md
+++ b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-86-cuboid-route.md
@@ -14,22 +14,40 @@ A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3, and a f
 
 However, there are up to three "shortest" path candidates for any given cuboid and the shortest route doesn't always have integer length.
 
-It can be shown that there are exactly 2060 distinct cuboids, ignoring rotations, with integer dimensions, up to a maximum size of M by M by M, for which the shortest route has integer length when M = 100. This is the least value of M for which the number of solutions first exceeds two thousand; the number of solutions when M = 99 is 1975.
+It can be shown that there are exactly `2060` distinct cuboids, ignoring rotations, with integer dimensions, up to a maximum size of M by M by M, for which the shortest route has integer length when M = 100. This is the least value of M for which the number of solutions first exceeds two thousand; the number of solutions when M = 99 is `1975`.
 
-Find the least value of M such that the number of solutions first exceeds one million.
+Find the least value of M such that the number of solutions first exceeds `n`.
 
 # --hints--
 
-`cuboidRoute()` should return a number.
+`cuboidRoute(2000)` should return a number.
 
 ```js
-assert(typeof cuboidRoute() === 'number');
+assert(typeof cuboidRoute(2000) === 'number');
 ```
 
-`cuboidRoute()` should return 1818.
+`cuboidRoute(2000)` should return `100`.
 
 ```js
-assert.strictEqual(cuboidRoute(), 1818);
+assert.strictEqual(cuboidRoute(2000), 100);
+```
+
+`cuboidRoute(25000)` should return `320`.
+
+```js
+assert.strictEqual(cuboidRoute(25000), 320);
+```
+
+`cuboidRoute(500000)` should return `1309`.
+
+```js
+assert.strictEqual(cuboidRoute(500000), 1309);
+```
+
+`cuboidRoute(1000000)` should return `1818`.
+
+```js
+assert.strictEqual(cuboidRoute(1000000), 1818);
 ```
 
 # --seed--
@@ -37,16 +55,40 @@ assert.strictEqual(cuboidRoute(), 1818);
 ## --seed-contents--
 
 ```js
-function cuboidRoute() {
+function cuboidRoute(n) {
 
   return true;
 }
 
-cuboidRoute();
+cuboidRoute(2000);
 ```
 
 # --solutions--
 
 ```js
-// solution required
+function cuboidRoute(n) {
+  // Based on https://www.mathblog.dk/project-euler-86-shortest-path-cuboid/
+  function getLength(a, b) {
+    return Math.sqrt(a ** 2 + b ** 2);
+  }
+
+  let M = 2;
+  let counter = 0;
+
+  while (counter < n) {
+    M++;
+    for (let baseHeightWidth = 3; baseHeightWidth <= 2 * M; baseHeightWidth++) {
+      const pathLength = getLength(M, baseHeightWidth);
+      if (Number.isInteger(pathLength)) {
+        if (baseHeightWidth <= M) {
+          counter += Math.floor(baseHeightWidth / 2);
+        } else {
+          counter += 1 + M - Math.floor((baseHeightWidth + 1) / 2);
+        }
+      }
+    }
+  }
+
+  return M;
+}
 ```