Advanced Reasoning Strategies / Reasoning Decomposition

Least-to-Most Prompting

Advanced [4/5]

Progressive problem solving Scaffolded reasoning

Definition

Least-to-Most prompting breaks complex problems into simpler subproblems, solving each sequentially from easiest to hardest. Each solution builds on previous ones, creating a scaffold that makes the final problem tractable.

This technique is particularly effective for problems that have natural hierarchical decomposition.

Key Concepts

Problem decomposition: Breaking down into ordered subproblems
Progressive complexity: Starting simple, building to complex
Solution chaining: Each answer feeds into the next
Scaffolded learning: Building understanding step by step

Examples

Math Problem

Building Block Approach

Original: "How many ways can 5 people sit in a row if
Alice and Bob must sit together?"

Decomposition:
Q1 (simplest): "How many ways can 2 people sit together?"
A1: 2 ways (AB or BA)

Q2: "If we treat Alice-Bob as one unit, how many units total?"
A2: 4 units (Alice-Bob + 3 others)

Q3: "How many ways can 4 units be arranged?"
A3: 4! = 24 ways

Q4 (original): "Combine previous answers"
A4: 2 × 24 = 48 ways

Two-Phase Process

Decompose Then Solve

Phase 1 - Decomposition Prompt:
"Break this problem into simpler subproblems that can
be solved sequentially: [complex problem]"

Phase 2 - Sequential Solving:
"Solve subproblem 1: [simplest problem]"
"Using that answer, solve subproblem 2: [next problem]"
...
"Using all previous answers, solve the final problem"

Interactive Exercise

✎

Decompose a Problem

Break this into least-to-most subproblems:

Problem: "Calculate the total cost of a road trip: 500 miles, car gets 25 mpg, gas costs $4/gallon, plus $50/night hotel for 2 nights."

Pro Tips

Start with the absolute simplest subproblem
Each step should clearly build on previous answers
Verify intermediate answers before proceeding
Works especially well for math and logic problems

Definition

Key Concepts

Examples

Interactive Exercise

Related Terms