32dbe23f5e
* fix: clean-up Project Euler 301-320 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
55 lines
1.7 KiB
Markdown
55 lines
1.7 KiB
Markdown
---
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id: 5900f49f1000cf542c50ffb1
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title: 'Problem 306: Paper-strip Game'
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challengeType: 5
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forumTopicId: 301960
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dashedName: problem-306-paper-strip-game
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---
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# --description--
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The following game is a classic example of Combinatorial Game Theory:
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Two players start with a strip of $n$ white squares and they take alternate turns. On each turn, a player picks two contiguous white squares and paints them black. The first player who cannot make a move loses.
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- $n = 1$: No valid moves, so the first player loses automatically.
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- $n = 2$: Only one valid move, after which the second player loses.
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- $n = 3$: Two valid moves, but both leave a situation where the second player loses.
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- $n = 4$: There are three valid moves for the first player; who is able to win the game by painting the two middle squares.
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- $n = 5$: Four valid moves for the first player (shown below in red); but no matter what the player does, the second player (blue) wins.
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<img class="img-responsive center-block" alt="valid starting moves for strip with 5 squares" src="https://cdn.freecodecamp.org/curriculum/project-euler/paper-strip-game.gif" style="background-color: white; padding: 10px;">
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So, for $1 ≤ n ≤ 5$, there are 3 values of $n$ for which the first player can force a win.
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Similarly, for $1 ≤ n ≤ 50$, there are 40 values of $n$ for which the first player can force a win.
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For $1 ≤ n ≤ 1\\,000\\,000$, how many values of $n$ are there for which the first player can force a win?
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# --hints--
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`paperStripGame()` should return `852938`.
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```js
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assert.strictEqual(paperStripGame(), 852938);
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```
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# --seed--
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## --seed-contents--
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```js
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function paperStripGame() {
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return true;
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}
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paperStripGame();
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```
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# --solutions--
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```js
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// solution required
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```
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