Least-to-Most Prompting
Complex problems become manageable when you break them into simpler pieces and solve them in order. Least-to-Most decomposes a hard question into easy sub-questions, solves each one progressively, and passes every answer forward — building a staircase of understanding from the ground up.
Introduced: Least-to-Most Prompting was published in 2022 by Zhou et al. at Google Research. The technique was designed to overcome a key limitation of chain-of-thought prompting: the inability to generalize to problems harder than those shown in the few-shot examples. Least-to-Most introduces a two-stage protocol — first decompose the complex problem into a sequence of simpler sub-problems, then solve each sub-problem from easiest to hardest, passing the context of previously solved sub-problems forward. The original paper demonstrated dramatic improvements on symbolic manipulation, compositional generalization (SCAN benchmark), and math word problems.
Modern LLM Status: The progressive decomposition strategy of Least-to-Most has been partially absorbed into modern LLM reasoning capabilities. Claude, GPT-4, and Gemini can often decompose problems implicitly when prompted with chain-of-thought. However, Least-to-Most’s explicit two-stage structure remains valuable when you need guaranteed decomposition before solving, when dealing with problems that require length generalization beyond the examples provided, or when each sub-problem’s solution must be independently verifiable. The technique is especially relevant for compositional tasks, multi-step math, and any domain where building from simple to complex is the natural problem-solving strategy.
Progressive Decomposition: Simple to Complex
Most complex problems are not monolithic — they are stacks of simpler problems in disguise. A multi-step math word problem, a long sequence of instructions, or a reading comprehension question spanning several paragraphs all share the same structure: solve the easy parts first, then use those answers to tackle the hard parts.
Least-to-Most formalizes this intuition into a two-stage process. In Stage 1, the model decomposes the original problem into an ordered list of sub-problems, arranged from simplest to most complex. In Stage 2, the model solves each sub-problem in order, and critically, the answer to each sub-problem is appended to the context before attempting the next one. This means each successive sub-problem benefits from all previously established answers.
Think of it like building a staircase. You don’t leap to the top floor — you lay one step at a time, and each new step rests on the ones beneath it. The final step reaches the answer that a single leap could never reliably achieve.
When a model attempts to solve a complex problem in a single pass, it must hold all dependencies, intermediate values, and logical connections in working memory simultaneously. This leads to dropped steps, arithmetic errors, and hallucinated shortcuts. Least-to-Most eliminates this cognitive overload by ensuring the model only ever faces a problem it can solve with the information already established — turning a high-wire act into a series of confident, grounded steps.
The Least-to-Most Process
Two stages from complex problem to reliable answer
Receive the Complex Problem
Start with a problem that is too complex or too long to solve reliably in a single step. These are typically problems with chained dependencies, compositional structures, or requirements that exceed what the model has seen in its few-shot examples.
“Amy has 4 times as many apples as Ben. Ben has 3 more apples than Carl. Carl has 2 apples. How many apples does Amy have?”
Stage 1: Decompose Into Ordered Sub-Problems
The model identifies the sub-problems hidden within the original question and orders them from simplest to most complex. Each sub-problem should be solvable using only the original information plus answers from earlier sub-problems. This decomposition step is what distinguishes Least-to-Most from standard chain-of-thought — the problem structure is made explicit before any solving begins.
Sub-problems identified:
1. How many apples does Carl have?
2. How many apples does Ben have?
3. How many apples does Amy have?
Stage 2: Solve Progressively, Passing Context Forward
Solve each sub-problem in order, starting with the easiest. After solving each one, append its answer to the context for the next sub-problem. This progressive accumulation of solved results means the model never faces a sub-problem without the prerequisite knowledge it needs. Each answer becomes a stepping stone for the next.
Q1: Carl has 2 apples (given directly).
Q2: Ben has 3 more than Carl. Carl has 2, so Ben has 2 + 3 = 5 apples.
Q3: Amy has 4 times as many as Ben. Ben has 5, so Amy has 5 × 4 = 20 apples.
Deliver the Final Answer
The answer to the final (most complex) sub-problem is the answer to the original question. Because every intermediate step was solved explicitly and its answer was carried forward, the final result is grounded in a verifiable chain of reasoning rather than an opaque leap of logic.
Final answer: Amy has 20 apples. The answer was built step by step: Carl (2) → Ben (5) → Amy (20).
See the Difference
Why progressive decomposition outperforms direct solving
Direct Solving
A train travels from City A to City B at 60 mph for the first leg, then from City B to City C at 90 mph for the second leg. The first leg is 180 miles and the second leg is 270 miles. A car leaves City A at the same time traveling directly to City C (a 400-mile route) at a constant speed. The car arrives 30 minutes after the train. How fast was the car going?
The car was traveling at about 72 mph. [Skips showing intermediate calculations, may confuse legs or misapply time calculations]
Least-to-Most
Sub-problem 1: How long does the train take for leg 1?
Answer: 180 miles / 60 mph = 3 hours.
Sub-problem 2: How long does the train take for leg 2?
Answer: 270 miles / 90 mph = 3 hours.
Sub-problem 3: What is the train’s total travel time?
Answer: 3 + 3 = 6 hours.
Sub-problem 4: How long does the car take?
Answer: 6 hours + 0.5 hours = 6.5 hours.
The car’s speed = 400 miles / 6.5 hours ≈ 61.5 mph. Each step is independently verifiable.
Practice Responsible AI
Always verify AI-generated content before use. AI systems can produce confident but incorrect responses. When using AI professionally, transparent disclosure is both best practice and increasingly a legal requirement.
48 US states now require AI transparency in key areas. Critical thinking remains your strongest tool against misinformation.
Least-to-Most in Action
See how progressive decomposition handles different problem types
“A store offers a 20% discount on all items. Sarah buys 3 shirts at $45 each and 2 pairs of pants at $60 each. She also has a coupon for $15 off her total after the discount. If tax is 8%, what is her final bill?”
Sub-problem 1: What is the pre-discount total?
Answer: Shirts: 3 × $45 = $135. Pants: 2 × $60 = $120. Total: $135 + $120 = $255.
Sub-problem 2: What is the total after the 20% discount?
Answer: Discount: $255 × 0.20 = $51. After discount: $255 − $51 = $204.
Sub-problem 3: What is the total after the $15 coupon?
Answer: $204 − $15 = $189.
Sub-problem 4: What is the final bill with 8% tax?
Answer: Tax: $189 × 0.08 = $15.12. Final bill: $189 + $15.12 = $204.12.
“Given the passage describing a company’s restructuring: The CEO announced that the marketing division would merge with sales, the resulting team would report to a new VP, and all affected employees would receive retention bonuses. How many organizational changes are described, and which change would have the most direct impact on day-to-day workflows?”
Sub-problem 1: What distinct organizational changes are described?
Answer: Three changes: (1) merging marketing with sales, (2) new VP reporting structure, (3) retention bonuses for affected employees.
Sub-problem 2: Which of these changes affect day-to-day workflows?
Answer: The merger directly changes who employees work with and what tasks they handle daily. The new VP changes the reporting line. Retention bonuses are one-time compensation with no workflow impact.
Sub-problem 3: Which change has the most direct daily impact?
Answer: The merger of marketing and sales has the most direct impact on day-to-day workflows, as it changes team composition, collaboration patterns, and potentially job responsibilities for everyone in both divisions. There are 3 organizational changes, and the division merger most directly affects daily work.
“Concatenate the last letter of each word in this sentence: Artificial intelligence transforms modern education.”
Sub-problem 1: What is the last letter of “Artificial”?
Answer: “l”
Sub-problem 2: What is the last letter of “intelligence”?
Answer: “e”
Sub-problem 3: What is the last letter of “transforms”?
Answer: “s”
Sub-problem 4: What is the last letter of “modern”?
Answer: “n”
Sub-problem 5: What is the last letter of “education”?
Answer: “n”
Final concatenation: l + e + s + n + n = “lesnn”
When to Use Least-to-Most
Best for problems with layered dependencies that benefit from progressive solving
Perfect For
Word problems with chained relationships where each value depends on previous calculations — the progressive context passing eliminates arithmetic drift.
Tasks that combine primitive operations into longer sequences — Least-to-Most enables solving sequences longer and harder than the examples provided.
When the target problem is significantly harder or longer than the few-shot examples — decomposition bridges the complexity gap that chain-of-thought cannot.
Any problem where the answer to one part is required input for the next — Least-to-Most makes the dependency order explicit and ensures nothing is skipped.
Skip It When
Problems solvable with one direct calculation or lookup — decomposition adds overhead without benefit when there is nothing to decompose.
When sub-problems are independent and don’t build on each other — Least-to-Most’s sequential context-passing adds no value if there are no dependencies between parts.
Writing, brainstorming, or subjective tasks where there is no objectively correct decomposition order — Least-to-Most is designed for structured, deterministic problem-solving.
Use Cases
Where Least-to-Most delivers the most value
Complex Debugging
Trace bugs through layered systems by first understanding expected behavior, then actual behavior, then isolating the discrepancy — each step building on the last.
Educational Tutoring
Teach students by decomposing hard problems into prerequisite concepts, ensuring mastery of each foundation before advancing to the next level of complexity.
Legal Analysis
Break regulatory compliance questions into jurisdiction-specific sub-questions, solving each dependency before combining them into a comprehensive legal assessment.
Financial Modeling
Build financial projections by solving base assumptions first, then intermediate calculations, then final projections — each layer grounded in verified prior results.
Compositional Instructions
Execute long command sequences like “turn left twice, jump, then run forward” by solving each primitive operation before combining them into the full sequence.
Scientific Problem-Solving
Tackle multi-variable science problems by solving for one variable at a time, using each established value to unlock the next calculation in the chain.
Where Least-to-Most Fits
Least-to-Most bridges linear reasoning and modular decomposition
Least-to-Most was originally demonstrated with few-shot examples for both the decomposition and solving stages. For maximum effectiveness, provide the model with 1–2 examples of how to decompose a similar problem and how to solve each sub-problem. This scaffolding helps the model learn the decomposition pattern for your specific domain, enabling it to generalize to harder problems than any single example covers.
Related Techniques
Explore complementary decomposition and reasoning techniques
Break Down Complex Problems
Try Least-to-Most decomposition on your own multi-step challenges or build structured prompts with our tools.