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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-459-flipping-game.md

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+---
+id: 5900f5371000cf542c51004a
+title: 'Problem 459: Flipping game'
+challengeType: 5
+forumTopicId: 302133
+dashedName: problem-459-flipping-game
+---
+
+# --description--
+
+The flipping game is a two player game played on a N by N square board.
+
+Each square contains a disk with one side white and one side black.
+
+The game starts with all disks showing their white side.
+
+A turn consists of flipping all disks in a rectangle with the following properties: the upper right corner of the rectangle contains a white disk the rectangle width is a perfect square (1, 4, 9, 16, ...) the rectangle height is a triangular number (1, 3, 6, 10, ...)
+
+Players alternate turns. A player wins by turning the grid all black.
+
+Let W(N) be the number of winning moves for the first player on a N by N board with all disks white, assuming perfect play. W(1) = 1, W(2) = 0, W(5) = 8 and W(102) = 31395.
+
+For N=5, the first player's eight winning first moves are:
+
+Find W(106).
+
+# --hints--
+
+`euler459()` should return 3996390106631.
+
+```js
+assert.strictEqual(euler459(), 3996390106631);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function euler459() {
+
+  return true;
+}
+
+euler459();
+```
+
+# --solutions--
+
+```js
+// solution required
+```