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problem-solver

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English
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Chinese

Problem Solver

问题解决工具

Structured problem-solving with step-by-step explanations.
结构化问题解决方法，附带分步解释。

Problem-Solving Framework

问题解决框架

mermaid
flowchart LR
    A[Understand] --> B[Plan]
    B --> C[Execute]
    C --> D[Verify]
    D -->|Error| B
    D -->|Correct| E[Explain]
mermaid
flowchart LR
    A[Understand] --> B[Plan]
    B --> C[Execute]
    C --> D[Verify]
    D -->|Error| B
    D -->|Correct| E[Explain]

Step 1: Understand (Identify)

步骤1：理解（识别）

Questions to Ask

需要提出的问题

  1. What is given? List all known information
  2. What is asked? Clearly state what to find
  3. What type of problem? Categorize (algebra, kinematics, etc.)
  4. What are the constraints? Any restrictions or conditions
  1. 已知条件是什么？ 列出所有已知信息
  2. 要求解什么？ 明确说明需要找到的内容
  3. 这是什么类型的问题？ 进行分类（代数、运动学等）
  4. 有哪些约束条件？ 任何限制或前提条件

Template

模板

markdown
**Given:**
- [List all known values with units]

**Find:**
- [What we need to calculate]

**Type:**
- [Problem category]
markdown
**已知：**
- [列出所有带单位的已知数值]

**求解：**
- [我们需要计算的内容]

**类型：**
- [问题类别]

Step 2: Plan (Strategy)

步骤2：规划（策略）

Choose Approach

选择方法

Problem TypeCommon Strategies
Equation solvingIsolation, substitution, factoring
Word problemsDefine variables, write equations
PhysicsDraw diagram, identify forces/energies
ProofsDirect, contradiction, induction
OptimizationTake derivative, find critical points
问题类型常用策略
解方程隔离法、代入法、因式分解法
文字应用题定义变量、列出方程
物理题绘制示意图、识别力/能量
证明题直接证明、反证法、归纳法
优化问题求导、寻找临界点

Write Steps (Before Executing)

列出执行步骤（在执行前）

  1. First, I will...
  2. Then, I will...
  3. Finally, I will...
  1. 首先，我会...
  2. 然后，我会...
  3. 最后，我会...

Step 3: Execute (Solve)

步骤3：执行（求解）

Show All Work

展示完整过程

markdown
**Step 1:** [Action]
[Mathematical work]
= [Result]

**Step 2:** [Action]
[Mathematical work]
= [Result]

**Step 3:** [Final calculation]
[Work]
= [Final answer with units]
markdown
**步骤1：** [操作]
[数学运算过程]
= [结果]

**步骤2：** [操作]
[数学运算过程]
= [结果]

**步骤3：** [最终计算]
[运算过程]
= [带单位的最终答案]

Best Practices

最佳实践

  • One step at a time
  • Include units throughout
  • Box or highlight final answer
  • Keep work organized vertically
  • 分步进行
  • 全程保留单位
  • 用方框或高亮标注最终答案
  • 保持运算过程纵向条理清晰

Step 4: Verify (Check)

步骤4：验证（检查）

Verification Methods

验证方法

MethodHow to Apply
Plug back inSubstitute answer into original equation
Units analysisCheck dimensions match expected result
EstimateIs the magnitude reasonable?
Alternate methodSolve differently, compare results
Edge casesDoes answer work at extremes?
方法应用方式
代入验证将答案代入原方程
单位分析检查维度是否与预期结果匹配
估算数值大小是否合理？
替代方法用不同方法求解，对比结果
边界情况答案在极端条件下是否成立？

Template

模板

markdown
**Check:**
- Substituting x = [answer] into original equation:
  [show substitution] = [expected value] ✓
- Units: [unit analysis]
- Reasonableness: [is the answer logical?]
markdown
**验证：**
- 将x = [答案]代入原方程：
  [展示代入过程] = [预期值] ✓
- 单位：[单位分析]
- 合理性：[答案是否符合逻辑？]

Teaching Modes

教学模式

Hint Mode

提示模式

Give progressive hints, not full solutions:
Hint 1: "What type of problem is this?" (Identification) Hint 2: "What formula relates these quantities?" (Direction) Hint 3: "Try isolating variable X first." (Specific guidance)
逐步给出提示，而非完整解答：
提示1： "这是什么类型的问题？"（识别阶段） 提示2： "哪些公式关联这些量？"（方向引导） 提示3： "先尝试隔离变量X。"（具体指导）

Socratic Mode

苏格拉底式引导模式

Guide through questions:
  • "What do you notice about the given information?"
  • "What principle applies here?"
  • "What would happen if you tried...?"
通过问题引导思考：
  • "你从已知信息中发现了什么？"
  • "这里适用什么原理？"
  • "如果你尝试...会发生什么？"

Full Solution Mode

完整解答模式

Complete step-by-step solution with explanations.
提供带解释的完整分步解决方案。

Common Problem Patterns

常见问题类型

Pattern 1: Solve for X

类型1：求解X

  1. Simplify both sides
  2. Collect X terms on one side
  3. Isolate X
  1. 化简等式两边
  2. 将含X的项移到一侧
  3. 隔离X

Pattern 2: Word Problem

类型2：文字应用题

  1. Define variables
  2. Translate words to equations
  3. Solve system of equations
  4. Answer in context
  1. 定义变量
  2. 将文字转化为方程
  3. 求解方程组
  4. 结合语境给出答案

Pattern 3: Rate Problem

类型3：速率问题

  1. Identify rate (units per time)
  2. Use: Amount = Rate × Time
  3. Set up equation and solve
  1. 识别速率（单位时间内的量）
  2. 使用公式：总量 = 速率 × 时间
  3. 建立方程并求解

Pattern 4: Optimization

类型4：优化问题

  1. Write objective function
  2. Take derivative
  3. Set equal to zero
  4. Solve for critical points
  5. Test for max/min
  1. 写出目标函数
  2. 求导
  3. 令导数等于0
  4. 求解临界点
  5. 测试最大值/最小值

Answer Template

答案模板

markdown
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markdown
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Problem

问题

[State the problem]
[陈述问题]

Solution

解决方案

Understanding

理解阶段

  • Given: [knowns]
  • Find: [unknown]
  • 已知： [已知条件]
  • 求解： [未知内容]

Approach

方法思路

[Brief strategy explanation]
[简要说明策略]

Work

运算过程

Step 1: [action] [calculation]
Step 2: [action] [calculation]
步骤1： [操作] [计算过程]
步骤2： [操作] [计算过程]

Answer

答案

[Final answer with units]
[带单位的最终答案]

Verification

验证

[Check work]
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[检查过程]
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