These 24 prompts are built for the one thing DeepSeek does best: hard reasoning. They run on DeepSeek-V3.2, the free, open-source flagship released in December 2025 with a 128K-token context window and gold-medal-level math scores. Each one is grouped by job — step-by-step reasoning, math problems, proofs, logic puzzles, probability, and optimization — and written out in full so you can copy, swap the [BRACKETS], and send.
The habit that makes all of them work: turn on DeepThink. DeepThink exposes the full chain-of-thought before the final answer, so DeepSeek reasons in the open instead of guessing — and you can catch a wrong assumption the moment it appears. Then always ask it to verify. A model can still slip on arithmetic, so ending with "verify your answer against the constraints" is what turns a plausible answer into a trustworthy one. New here? Start with the DeepSeek prompt roundup and the deeper guide to prompting DeepSeek for reasoning.
Step-by-step reasoning
The core formula for DeepSeek is Problem + Context + Constraints + "show reasoning, then verify". Give it the hard problem plainly, not a rigid template, and let DeepThink do the work in the open.
1. Work any hard problem step by step
Turn on DeepThink. Here is the problem: [PROBLEM]. Context: [ANY BACKGROUND]. Constraints: [LIST ALL CONSTRAINTS]. Think step by step and show every step of your reasoning. Define your variables before you use them, state any assumption you make, and consider more than one approach before committing. Verify your answer against the constraints before giving the final result.Why it works: This is the master template — DeepThink plus "show every step, define variables, verify" covers almost any reasoning task in one go.
2. Solve it two different ways
Turn on DeepThink. Solve this problem using two independent methods: [PROBLEM]. Show the full working for each method separately. If both methods give the same answer, say so and give the final result. If they disagree, find where the discrepancy comes from and resolve it before answering. Verify the final answer against the original numbers.Why it works: Two independent paths that must agree is one of the strongest self-checks there is; it catches errors a single pass would miss.
3. Reason from stated constraints
Turn on DeepThink. Given only these facts and constraints, work out what must be true: [LIST FACTS AND CONSTRAINTS]. Reason step by step, and for each conclusion cite exactly which facts force it. Do not add outside assumptions. If the facts are not enough to reach a definite answer, say what is undetermined and what extra information would settle it.Best for: Deductive problems where the answer follows strictly from given rules, not from general knowledge.
4. Find the flaw in an argument
Turn on DeepThink. Here is an argument that claims to prove [CLAIM]: [PASTE ARGUMENT]. Go through it step by step and decide whether the conclusion actually follows. Identify any invalid step, hidden assumption, or logical fallacy by name. If the argument is sound, explain why. If it is flawed, show the exact step that breaks and what would be needed to fix it.Why it works: Naming the exact failing step forces DeepSeek to audit the logic rather than react to whether it agrees with the conclusion.
Math problems
For calculation, DeepThink keeps the algebra visible so a wrong line is easy to spot. State the problem and any units, then demand a verify step at the end.
5. Algebra and equation solver
Turn on DeepThink. Solve this: [EQUATION OR SYSTEM]. Show every algebraic step, do not skip any line, and state each rule you apply (factoring, substitution, etc.). Give all valid solutions and reject any extraneous ones, saying why. Then verify by substituting each solution back into the original equation and confirming it holds.Why it works: "Substitute the solution back in" is a built-in check that catches sign errors and extraneous roots automatically.
6. Word problem to equations
Turn on DeepThink. Solve this word problem: [PROBLEM]. First, define every variable in one line each and write down what quantity it represents with units. Translate the words into equations, showing which sentence gives which equation. Solve step by step, keep units throughout, and verify the final answer makes sense in the real-world context before stating it.Best for: Turning messy word problems into clean equations without losing track of what each number means.
7. Calculus step-through
Turn on DeepThink. Work this calculus problem step by step: [DERIVATIVE / INTEGRAL / LIMIT]. Name the rule at each step (chain rule, product rule, u-substitution, etc.) and show the intermediate expression. If a step has a common pitfall, flag it. For a definite integral or limit, verify the result with a quick sanity check or an alternate method before giving the final answer.Why it works: Naming the rule at each step exposes where a chain-rule or substitution mistake would hide.
8. Estimation and sanity check
Turn on DeepThink. Estimate the answer to this before solving exactly: [PROBLEM]. First give a rough order-of-magnitude estimate and explain the assumptions behind it. Then solve it precisely, showing your steps. Compare the exact answer to your estimate: if they are far apart, find out which one is wrong and explain why. Give the verified final answer.Best for: Big-number or real-world problems where an order-of-magnitude gut check catches gross mistakes fast.
Proofs & derivations
DeepSeek handles induction, contradiction, and epsilon-delta proofs with DeepThink on. Tell it which technique to try and make it check that no step assumes the conclusion.
9. Proof by induction
Turn on DeepThink. Prove the following statement by mathematical induction: [STATEMENT]. Clearly separate the base case and the inductive step. State the inductive hypothesis explicitly, show exactly where you use it, and complete the algebra in full. At the end, verify the base case numerically and re-read the inductive step to confirm it does not assume what it is trying to prove.Why it works: Separating base case, hypothesis, and step, then re-checking for circular reasoning, produces a proof you can actually trust.
10. Proof by contradiction
Turn on DeepThink. Prove this by contradiction: [STATEMENT]. State the assumption you are negating in plain language first. Reason step by step until you reach a clear contradiction, and name exactly which established fact or definition the contradiction violates. Then confirm the logic runs cleanly from the negated assumption to the contradiction with no gaps before stating the conclusion.Best for: Statements about irrationality, infinitude, or impossibility where assuming the opposite is the natural attack.
11. Derive a formula from scratch
Turn on DeepThink. Derive [FORMULA / RESULT] from first principles, starting only from [STARTING DEFINITIONS OR AXIOMS]. Show every step and justify each move with the definition or theorem it relies on. Do not quote the final formula as a known fact along the way. When you reach the result, verify it by checking a simple known case where you already know the answer.Why it works: Forbidding it from quoting the target formula mid-derivation forces a genuine build-up instead of reverse-engineering.
12. Check a proof for gaps
Turn on DeepThink. Here is a proof of [CLAIM]: [PASTE PROOF]. Check it line by line. For each step, decide whether it truly follows from the previous ones and note any unstated assumption, missing case, or logical gap. If the proof is valid, say so and summarize why. If it is broken, identify the first faulty step and explain precisely what is wrong.Best for: Grading your own draft proof, or a proof you found, before you rely on it.
Logic & puzzles
Puzzles reward slow, explicit reasoning — exactly what DeepThink provides. Ask DeepSeek to track its state and rule out possibilities one at a time rather than leaping to an answer. The DeepSeek coding prompts use the same show-your-work discipline for code.
13. Classic logic puzzle
Turn on DeepThink. Solve this logic puzzle: [PUZZLE]. List the entities and every clue first. Then work through the clues one at a time, and after each clue state what you can now rule out or lock in. Do not guess. When you reach a full solution, re-read all the original clues and confirm the solution satisfies every single one before presenting it.Why it works: Updating state after each clue and re-reading every clue at the end is how DeepThink avoids the classic "almost right" puzzle answer.
14. Constraint satisfaction grid
Turn on DeepThink. This is a grid / matching puzzle: [DESCRIBE CATEGORIES AND CLUES]. Set up the possibilities as a grid and eliminate systematically, showing the grid state as it changes at key points. Explain the deduction behind every elimination. If the clues force a unique solution, present it; if more than one solution fits, list them all and note which clue would break the tie.Best for: "Who owns the zebra" style puzzles with categories that must be matched under many clues.
15. Knights and knaves
Turn on DeepThink. Solve this knights-and-knaves problem, where knights always tell the truth and knaves always lie: [PUZZLE]. Consider each possible assignment of knight or knave to the characters, and for each, check whether every statement is consistent. Eliminate the impossible cases with reasons. State the unique consistent assignment, and verify it by re-testing every statement against it.Why it works: Casework over every truth-teller/liar assignment, each fully tested, is exactly the exhaustive method these puzzles need.
16. Sequence and pattern finder
Turn on DeepThink. Find the rule behind this sequence and give the next [3] terms: [SEQUENCE]. Consider several candidate patterns (differences, ratios, position-based formulas, interleaved sequences) rather than settling on the first that seems to fit. State the rule you chose, why it beats the alternatives, and verify it reproduces every given term before extending the sequence.Best for: Number and pattern puzzles where the obvious rule is often not the intended one.
Probability & statistics
Probability is where quick intuition fails most often, so DeepThink and an explicit verify step earn their keep. Make DeepSeek define the sample space before it computes anything.
17. Probability with full reasoning
Turn on DeepThink. Compute the probability for this problem: [PROBLEM]. First define the sample space and state whether events are independent, mutually exclusive, or conditional. Show the formula you use and every step of the calculation. Then verify: check the answer is between 0 and 1, and if there is a complementary or alternate route to the same number, use it to confirm the result.Why it works: Defining the sample space first and cross-checking with the complement catches the intuition traps that make probability so error-prone.
18. Bayesian update
Turn on DeepThink. Apply Bayes' theorem to this: [PRIOR, EVIDENCE, AND LIKELIHOODS]. Write out the prior, the likelihood, and the evidence term explicitly, then compute the posterior step by step. Show the numbers plugged into Bayes' theorem, not just the final figure. Verify that the posteriors across all hypotheses sum to 1, and give a one-line plain-English reading of the result.Best for: Medical-test, spam-filter, and diagnostic problems where base rates flip the intuitive answer.
19. Counting and combinatorics
Turn on DeepThink. Count the number of ways for this: [PROBLEM]. Decide first whether order matters and whether repetition is allowed, and say so. Choose permutations, combinations, or a case split accordingly, and explain the choice. Show the arithmetic. Then verify by counting a small version of the problem by hand and confirming your formula gives the same number.Why it works: The "does order matter, is repetition allowed" checklist plus a small-case check prevents the most common counting mistakes.
20. Interpret a statistical result
Turn on DeepThink. Here is a statistical result: [PASTE RESULT — e.g. p-value, confidence interval, effect size, or correlation]. Explain in plain language what it does and does not mean. Reason through common misinterpretations (correlation vs causation, what a p-value is not, sample-size effects) and say which apply here. End with a cautious, honest one-paragraph takeaway a non-statistician can trust.Best for: Making sense of a study or A/B test result without over-claiming what the numbers show.
Decisions & optimization
For decisions and optimization, DeepThink lets you watch the trade-offs get weighed. State the objective and every constraint, then have DeepSeek check the answer really satisfies them all.
21. Decision under uncertainty
Turn on DeepThink. Help me decide between these options: [OPTIONS]. My goal is [GOAL] and the uncertainties are [WHAT I DON'T KNOW]. Lay out the possible outcomes for each option, estimate rough probabilities and payoffs, and compute the expected value where it helps. Reason through the downside risk, not just the average. Recommend one option and verify the recommendation still holds if a key assumption is off.Why it works: Expected value plus a downside check and an assumption stress-test gives a decision that survives being wrong about one input.
22. Constrained optimization
Turn on DeepThink. Optimize this: maximize/minimize [OBJECTIVE] subject to these constraints: [LIST CONSTRAINTS]. Define your variables, write the objective and every constraint as an expression, and solve step by step (show the method). Give the optimal values and the resulting objective. Then verify the solution satisfies every constraint exactly, and confirm no nearby feasible point does better.Best for: Budget, allocation, and scheduling problems with a clear objective and hard limits.
23. Compare options with a scoring model
Turn on DeepThink. Build a weighted scoring model to compare these options: [OPTIONS]. My criteria and how much each matters: [CRITERIA WITH ROUGH WEIGHTS]. Score each option on each criterion with a one-line justification, apply the weights, and show the math for the totals. Present a ranked table. Then verify: if I nudge the weights slightly, does the winner change? Note how sensitive the result is.Why it works: Showing the weighted math and testing weight sensitivity keeps the ranking honest instead of hiding a close call.
24. Resource allocation plan
Turn on DeepThink. I have [RESOURCE — e.g. budget, hours, headcount] to split across [ITEMS / PROJECTS] to maximize [GOAL], with these limits: [CONSTRAINTS]. Reason through the trade-offs, allocate the resource step by step, and explain why each amount goes where it does. Show that the total does not exceed the resource and that every constraint is met. Verify the allocation beats one or two obvious alternatives.Best for: Splitting a fixed budget or time across competing priorities with the reasoning laid bare.
Save this set for any hard problem, and keep the full DeepSeek prompt roundup handy for writing, coding, and research packs too. The one habit worth repeating: DeepThink on, show every step, verify at the end.
Frequently Asked Questions
Which DeepSeek model are these prompts built for?
They target DeepSeek-V3.2, the flagship released in December 2025, with a 128K-token context window and gold-medal-level math and reasoning comparable to GPT-5-class models. It is free and open-source (MIT) at chat.deepseek.com. Everything here also works on earlier V3 releases, since DeepThink is the shared feature that matters.
Why does DeepThink matter so much for math?
The DeepThink toggle exposes the full chain-of-thought before the final answer. For math and logic that means DeepSeek works the problem out in the open instead of jumping to a guess, so it catches its own mistakes and you can see exactly where an answer comes from. Turn it on for every hard reasoning task.
How do I make DeepSeek show every step?
Turn on DeepThink, then say "think step by step and show every step", "define your variables", and "do not skip any algebra". State the problem and every constraint up front. Giving it the hard problem plainly beats forcing a rigid output template.
Can I trust the answer, or should I add a verify step?
Always add a verify step. End every hard prompt with "verify your answer against the constraints before giving the final result." Even with DeepThink, a model can make an arithmetic slip, so asking it to plug the answer back in and check units and edge cases catches most errors before you rely on them.
Can DeepSeek write real proofs?
Yes. With DeepThink on it handles induction, contradiction, contrapositive, and epsilon-delta proofs and will justify each step. Tell it which proof technique to try, ask it to state assumptions explicitly, and have it check that no step secretly assumes the conclusion. Review the logic yourself before submitting anything graded.
Can I upload a problem set or PDF?
Yes. Use file upload to attach a problem set, worksheet, or PDF, then ask DeepSeek to solve each problem step by step with DeepThink on and verify each answer. For facts that must be current, turn on the Search toggle instead.
How do the [BRACKET] placeholders work?
Anything in square brackets is a swap-in. Replace [PROBLEM], [CONSTRAINTS], or [THEOREM] with your own details before sending. The rest of each prompt is written to be copy-paste ready.