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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-409-nim-extreme.md

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+---
+id: 5900f5061000cf542c510017
+title: 'Problem 409: Nim Extreme'
+challengeType: 5
+forumTopicId: 302077
+dashedName: problem-409-nim-extreme
+---
+
+# --description--
+
+Let n be a positive integer. Consider nim positions where:There are n non-empty piles.
+
+Each pile has size less than 2n.
+
+No two piles have the same size.
+
+Let W(n) be the number of winning nim positions satisfying the above
+
+conditions (a position is winning if the first player has a winning strategy). For example, W(1) = 1, W(2) = 6, W(3) = 168, W(5) = 19764360 and W(100) mod 1 000 000 007 = 384777056.
+
+Find W(10 000 000) mod 1 000 000 007.
+
+# --hints--
+
+`euler409()` should return 253223948.
+
+```js
+assert.strictEqual(euler409(), 253223948);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function euler409() {
+
+  return true;
+}
+
+euler409();
+```
+
+# --solutions--
+
+```js
+// solution required
+```