逻辑推理（跨域）

考什么 · What it tests

需要先会 · Prerequisites

• 分类讨论 / Casework
• 排除法与假设法 / Elimination and assumption
• 读题提取条件 / Extracting conditions from the text

常见套路 · Common moves

1. 正难则反，倒着推：从结论或最后一步往回推，比从头正推分支少——逆向推理是这类题最省力的通用招。

   When forward is hard, go backwards: reasoning from the conclusion or the last step branches less than pushing forward — working backwards is the most economical general move here.
2. 极端情形先试：要「最多/最少」时，先把某个量推到极端（最大或最小），边界往往就是答案。

   Test the extremes first: for "most/least," push a quantity to its limit (largest or smallest) — the boundary is often the answer.
3. 列表格锁死条件：多个对象多个属性配对（谁住几号、谁养什么）时画网格，逐条排除「不可能」。

   Pin conditions down with a grid: when matching several objects to several attributes (who lives where, who owns what), draw a table and cross out the impossible cells one by one.

易错点 · Common pitfalls

• 分类讨论漏掉某一类，或几类之间有重叠——分类必须「不重不漏」，先想清分类标准。

  Missing a case or letting cases overlap — casework must be exhaustive and disjoint, so settle the dividing rule first.
• 把「不是 $A$」直接当成「是 $B$」：只有在明确只有两种可能时才成立，否则会漏第三种情况。

  Reading "not $A$" as "therefore $B$": valid only when exactly two options exist — otherwise you miss a third possibility.