problem-solver

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Step-by-step problem solving with detailed explanations. Uses structured approach (Identify, Plan, Execute, Verify) for math, physics, chemistry, and CS problems. Can provide hints before solutions. Use when solving academic problems, working through practice questions, or learning problem-solving methods. Triggers - solve problem, step by step, show work, explain solution, how to solve, problem help.

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npx skill4agent add szeyu/vibe-study-skills problem-solver

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Translated version includes tags in frontmatter
problem-solvingstructured-learningacademic-supportstep-by-step-guidancehint-based-assistance

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Problem Solver

Structured problem-solving with step-by-step explanations.

Problem-Solving Framework

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

Step 1: Understand (Identify)

Questions to Ask

  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

Template

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

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

**Type:**
- [Problem category]

Step 2: Plan (Strategy)

Choose Approach

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

Write Steps (Before Executing)

  1. First, I will...
  2. Then, I will...
  3. Finally, I will...

Step 3: Execute (Solve)

Show All Work

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

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

**Step 3:** [Final calculation]
[Work]
= [Final answer with units]

Best Practices

  • One step at a time
  • Include units throughout
  • Box or highlight final answer
  • Keep work organized vertically

Step 4: Verify (Check)

Verification Methods

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?

Template

markdown
**Check:**
- Substituting x = [answer] into original equation:
  [show substitution] = [expected value] ✓
- Units: [unit analysis]
- Reasonableness: [is the answer logical?]

Teaching Modes

Hint Mode

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)

Socratic Mode

Guide through questions:
  • "What do you notice about the given information?"
  • "What principle applies here?"
  • "What would happen if you tried...?"

Full Solution Mode

Complete step-by-step solution with explanations.

Common Problem Patterns

Pattern 1: Solve for X

  1. Simplify both sides
  2. Collect X terms on one side
  3. Isolate X

Pattern 2: Word Problem

  1. Define variables
  2. Translate words to equations
  3. Solve system of equations
  4. Answer in context

Pattern 3: Rate Problem

  1. Identify rate (units per time)
  2. Use: Amount = Rate × Time
  3. Set up equation and solve

Pattern 4: Optimization

  1. Write objective function
  2. Take derivative
  3. Set equal to zero
  4. Solve for critical points
  5. Test for max/min

Answer Template

markdown
## Problem
[State the problem]

## Solution

### Understanding
- **Given:** [knowns]
- **Find:** [unknown]

### Approach
[Brief strategy explanation]

### Work
**Step 1:** [action]
[calculation]

**Step 2:** [action]
[calculation]

### Answer
**[Final answer with units]**

### Verification
[Check work]