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{
"data": {
"question": {
"questionId": "1086",
"questionFrontendId": "1025",
"categoryTitle": "Algorithms",
"boundTopicId": 3639,
"title": "Divisor Game",
"titleSlug": "divisor-game",
"content": "<p>Alice and Bob take turns playing a game, with Alice starting first.</p>\n\n<p>Initially, there is a number <code>n</code> on the chalkboard. On each player&#39;s turn, that player makes a move consisting of:</p>\n\n<ul>\n\t<li>Choosing any <code>x</code> with <code>0 &lt; x &lt; n</code> and <code>n % x == 0</code>.</li>\n\t<li>Replacing the number <code>n</code> on the chalkboard with <code>n - x</code>.</li>\n</ul>\n\n<p>Also, if a player cannot make a move, they lose the game.</p>\n\n<p>Return <code>true</code> <em>if and only if Alice wins the game, assuming both players play optimally</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> true\n<strong>Explanation:</strong> Alice chooses 1, and Bob has no more moves.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3\n<strong>Output:</strong> false\n<strong>Explanation:</strong> Alice chooses 1, Bob chooses 1, and Alice has no more moves.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 1000</code></li>\n</ul>\n",
"translatedTitle": "除数博弈",
"translatedContent": "<p>爱丽丝和鲍勃一起玩游戏,他们轮流行动。爱丽丝先手开局。</p>\n\n<p>最初,黑板上有一个数字&nbsp;<code>n</code>&nbsp;。在每个玩家的回合,玩家需要执行以下操作:</p>\n\n<ul>\n\t<li>选出任一&nbsp;<code>x</code>,满足&nbsp;<code>0 &lt; x &lt; n</code>&nbsp;且&nbsp;<code>n % x == 0</code>&nbsp;。</li>\n\t<li>用 <code>n - x</code>&nbsp;替换黑板上的数字&nbsp;<code>n</code> 。</li>\n</ul>\n\n<p>如果玩家无法执行这些操作,就会输掉游戏。</p>\n\n<p><em>只有在爱丽丝在游戏中取得胜利时才返回&nbsp;<code>true</code>&nbsp;。假设两个玩家都以最佳状态参与游戏。</em></p>\n\n<p>&nbsp;</p>\n\n<ol>\n</ol>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 2\n<strong>输出:</strong>true\n<strong>解释:</strong>爱丽丝选择 1鲍勃无法进行操作。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 3\n<strong>输出:</strong>false\n<strong>解释:</strong>爱丽丝选择 1鲍勃也选择 1然后爱丽丝无法进行操作。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 1000</code></li>\n</ul>\n",
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"hints": [
"If the current number is even, we can always subtract a 1 to make it odd. If the current number is odd, we must subtract an odd number to make it even."
],
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