Fix: Problem 39: Integer right triangles (#38145)

* fix: correct test and add solution

I also changed the seed to report the results of an easier example to
the user, since just evaluating the function mostly wastes time.

* fix: use a better solution

* fix: credit original author

curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-39-integer-right-triangles.english.md

@@ -24,8 +24,8 @@ For which value of p ≤ n, is the number of solutions maximised?
 tests:
   - text: <code>intRightTriangles(500)</code> should return 420.
     testString: assert(intRightTriangles(500) == 420);
-  - text: <code>intRightTriangles(800)</code> should return 420.
-    testString: assert(intRightTriangles(800) == 420);
+  - text: <code>intRightTriangles(800)</code> should return 720.
+    testString: assert(intRightTriangles(800) == 720);
   - text: <code>intRightTriangles(900)</code> should return 840.
     testString: assert(intRightTriangles(900) == 840);
   - text: <code>intRightTriangles(1000)</code> should return 840.
@@ -46,7 +46,7 @@ function intRightTriangles(n) {
   return n;
 }
 
-intRightTriangles(1000);
+console.log(intRightTriangles(500)); // 420
 ```
 
 </div>
@@ -59,7 +59,34 @@ intRightTriangles(1000);
 <section id='solution'>
 
 ```js
-// solution required
+
+// Original idea for this solution came from
+// https://www.xarg.org/puzzle/project-euler/problem-39/
+
+function intRightTriangles(n) {
+  // store the number of triangles with a given perimeter
+  let triangles = {};
+  // a is the shortest side
+  for (let a = 3; a < n / 3; a++)
+  // o is the opposite side and is at least as long as a
+    for (let o = a; o < n / 2; o++) {
+      let h = Math.sqrt(a * a + o * o); // hypotenuse
+      let p = a + o + h;  // perimeter
+      if ((h % 1) === 0 && p <= n) {
+        triangles[p] = (triangles[p] || 0) + 1;
+      }
+    }
+
+  let max = 0, maxp = null;
+  for (let p in triangles) {
+    if (max < triangles[p]) {
+      max = triangles[p];
+      maxp = p;
+    }
+  }
+  return maxp;
+}
+
 ```
 
 </section>