The cognitive reflection test (CRT) is a short reasoning measure built around questions with tempting wrong answers. Shane Frederick introduced the original three-item version in 2005 to investigate whether people reconsider an immediate response. This guide lets you try the problems, check the reasoning, and interpret your result. Frederick’s original paper provides the research foundation.
This is an educational walkthrough, not an IQ assessment. Your most useful takeaway is a method for checking an answer that feels obvious.
Try the three questions now → Write down your answers before opening the explanations.
Try the Cognitive Reflection Test: Three Questions
Write down your answers before opening the solutions. For this exercise, try without a calculator or outside help; there is no countdown. Note whether you have encountered any question before. These are paraphrased educational adaptations of the three problems in Frederick’s original CRT, preserving their numerical relationships.
1. The bat-and-ball problem
You spend $1.10 on a bat and a ball together. The bat’s price exceeds the ball’s price by $1.00. What is the ball’s price?
2. The machines problem
Five identical machines produce five widgets in five minutes. With the same production rate, how many minutes would 100 machines need to produce 100 widgets?
3. The lily-pad problem
A lily-pad patch doubles its covered area daily. On day 48, it covers the entire lake. On which day was the lake half covered?
Cognitive Reflection Test Answers Explained
Ready to check? Open the section below for the answer key and worked solutions. If your answer differs, compare your method with the conditions in the question.
Reveal the three answers and step-by-step explanations
| Problem | Tempting answer | Correct answer |
|---|---|---|
| Bat and ball | 10 cents | 5 cents |
| Machines | 100 minutes | 5 minutes |
| Lily pads | Day 24 | Day 47 |
Bat-and-ball answer: the ball costs 5 cents
Check what happens if the ball costs $0.10. The bat must cost $1.10 to be exactly $1.00 more expensive. Together, they would cost $1.20, which exceeds the stated total.
Instead, subtract the $1.00 price difference from the $1.10 total. The remaining $0.10 represents two copies of the ball’s price: one for the ball and one for the part of the bat’s price below its $1.00 premium. Divide that remainder by two.
- Ball: $0.10 ÷ 2 = $0.05.
- Bat: $0.05 + $1.00 = $1.05.
- Total: $0.05 + $1.05 = $1.10.
- Difference: $1.05 − $0.05 = $1.00.
If you prefer algebra, let the ball’s price be x. Then x + (x + 1.00) = 1.10, so 2x = 0.10 and x = 0.05. The essential check is that your answer satisfies both the total and the difference.
Machines answer: 5 minutes
The intended model has identical machines working simultaneously at a constant rate. If five machines make five widgets in five minutes, each machine makes one widget during that interval.
With 100 machines, all 100 widgets can therefore be produced in the same five-minute interval. Relative to the original setup, machine count and required output both increase twentyfold. The time remains unchanged.
The tempting 100-minute answer increases the required output while overlooking the additional machines. A useful check is to write the rate per machine: one widget every five minutes.
This answer assumes no extra setup delay, resource shortage, or shared bottleneck. Those assumptions belong to the puzzle. In an actual factory or project, you would need to verify them before scaling an estimate.
Lily-pad answer: day 47
Work backward from the fully covered lake. Because the patch doubles in area each day, it must have covered half the lake one day before full coverage.
Day 47: 50% coverage. Day 48: 100% coverage. One more doubling turns half into the whole.
Day 24 comes from halving the elapsed time. That would fit a different model in which the patch added the same area every day. Here, it multiplies its area instead. The quantity being doubled is coverage, not the day number.
As another check, move backward once more: the patch covers one-quarter of the lake on day 46. A quarter becomes a half, then a whole, over the final two daily doublings.
What Does Your CRT Score Mean?
For these three questions, give yourself one point per correct answer. The resulting score runs from 0 to 3. It records how many items you answered correctly on this attempt; it does not explain how you reached each answer.
| Score | What it records | Useful next step |
|---|---|---|
| 0 | No correct answers | Choose one solution and verify each step. |
| 1 | One correct answer | Compare your approach across the three questions. |
| 2 | Two correct answers | Identify the condition missed in the remaining problem. |
| 3 | All three answers correct | Explain each solution and note any prior familiarity. |
The next steps are editorial learning suggestions, not psychological classifications. We do not convert the result into an IQ, a percentile, or a permanent “intuitive” or “analytical” identity.
What Can the Cognitive Reflection Test Measure?
Both reflection and mathematical ability matter
It takes numerical understanding to solve these problems, but the research does not reduce neatly to “just mathematics.” Campitelli and Gerrans (2014) modeled responses from 2,019 participants. Models incorporating both mathematical processing and inhibition of an intuitive response fitted their data better than a model with mathematics alone.
For this walkthrough, the practical distinction is between noticing that an answer might be wrong and knowing how to check it. You can pause over the bat-and-ball problem and still need help representing the price relationship. Reviewing the arithmetic addresses that specific difficulty.
Familiarity affects interpretation
If you already know an answer, reporting it cannot show how you would solve the problem on a first encounter. However, familiarity does not automatically make the CRT useless for research. Białek and Pennycook (2018; first published online in 2017) examined six datasets with approximately 2,500 participants. Prior exposure was associated with higher scores, but they found no significant reduction in predictive power across the variables they examined.
Keep the two questions separate: what a remembered answer tells you about your own attempt, and whether scores remain associated with other measures across a research sample.
A correct answer does not reveal a single thinking process
The story “first an error, then reflection, then correction” is one possible route. It is not established by a correct answer alone. An eye-tracking study by Purcell and colleagues (2022; online in 2021) found evidence consistent with intuitive correct responding and uncertainty among people giving heuristic answers.
That finding complicates the idea that all correct answers must result from suppressing a wrong response. On this page, recording whether you calculated, guessed, or recalled an answer can aid reflection, but your account is not a laboratory measurement of the underlying process.
Three items cannot provide a complete personal profile
The original test offers only four possible total scores. Białek and Pennycook also discuss its short length, limited reliability, and restricted score range. These limitations matter when interpreting small differences between people. Their discussion supports continued development of expanded measures.
A blog exercise is best used to inspect particular reasoning moves. It cannot establish how reliably you will handle an unfamiliar workplace dilemma or judge another person’s intentions.
Does the Test Show That Intuition Is Unreliable?
No universal conclusion about intuition follows from these three problems. They demonstrate specific ways a plausible response can miss a condition. They do not sample every situation in which a judgment arrives quickly.
It helps to distinguish the concepts. System 1 and System 2 thinking provides a framework for discussing automatic and deliberate processing. Intuitive reasoning concerns judgments that arise without an accessible chain of deliberate steps. Heuristic thinking examines simplifying strategies. These topics overlap, but none is a score label.
Use the CRT to ask, “Does this answer fit all the information?” For the separate question of when experience can support a reliable judgment, explore expert intuition. Treating all fast answers as equally trustworthy—or equally suspect—would skip the context that needs examining.
How to Check a First Answer in Everyday Decisions
The following four steps are an editorial learning aid, not a validated assessment or a promise of better outcomes.
- State your first answer. Write the initial estimate or judgment clearly enough to examine.
- Identify the assumption. Ask what must be true for it to work.
- Perform a relevant check. Calculate, inspect evidence, or clarify a fact that bears on the assumption.
- Retain or revise the answer. Let the result determine whether a change is warranted.
Worked example: can three reviewers finish in one hour?
This is a hypothetical delivery-planning example, not a reported study. One reviewer completes six document reviews in three hours. You initially estimate that three reviewers could finish the same six reviews in one hour.
First, state the assumption: the work can be divided into independent reviews, all three people work at the same rate, and everyone can start immediately. At two reviews per person per hour, three reviewers could indeed complete six in an hour under those conditions.
Then check the workflow. Suppose every document also needs approval from one shared specialist, taking ten minutes per document. If that final approval starts only after all initial reviews finish, it adds an hour to the schedule. The overall task now takes two hours in this simplified scenario.
The initial calculation was useful but described only one stage. The check revealed a missing constraint. If no shared approval stage existed, the same review could instead support the original estimate.
Choose a stopping point: here, establish the review rate, independence of tasks, and approval sequence before committing to a time. Repeating the estimate without checking those conditions would add little.
Frequently Asked Questions
What is the cognitive reflection test?
It is a short set of reasoning problems used to study responses to tempting answers. The original CRT has three numerical questions. This page provides an educational adaptation with explanations.
What are the three CRT answers?
Show the answer-only recap
For the questions above: the ball costs 5 cents; the machines need 5 minutes; and the lake is half covered on day 47. Answers depend on the exact quantities and conditions, so check altered versions separately.
Is the cognitive reflection test an IQ test?
No. This three-question exercise does not provide an IQ score. Numerical reasoning contributes to performance, but converting your result into an intelligence label would go beyond what this walkthrough establishes.
What does a score of 3 mean?
You answered all three items correctly. It does not establish that you always reason carefully or make accurate everyday decisions. Consider whether you calculated the answers, remembered them, or reached them another way.
Does knowing the questions affect the result?
Record prior familiarity when interpreting your attempt. Research has found higher scores among previously exposed participants, while also finding that predictive relationships can remain. See the research discussion above for that distinction.
Can I improve my performance?
You can learn how to solve these particular problems and verify the arithmetic. Once you know the solutions, a higher retest score does not by itself demonstrate a broader improvement in reasoning. For further practice, explain a solution in your own words and check whether its assumptions hold in a different example.
To continue exploring how you judge and check information, visit our intuition games guide. Focus on the feedback each exercise provides and what it can help you examine.
Research Sources
- Frederick, S. (2005). Cognitive Reflection and Decision Making. Journal of Economic Perspectives, 19(4), 25–42. Original CRT and research context.
- Campitelli, G., & Gerrans, P. (2014). Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach. Memory & Cognition, 42, 434–447. Mathematics and inhibition in CRT performance.
- Białek, M., & Pennycook, G. (2018). The cognitive reflection test is robust to multiple exposures. Behavior Research Methods, 50, 1953–1959. First published online in 2017. Prior exposure and predictive validity.
- Purcell, Z. A., Howarth, S., Wastell, C. A., Roberts, A. J., & Sweller, N. (2022). Eye tracking and the cognitive reflection test: Evidence for intuitive correct responding and uncertain heuristic responding. Memory & Cognition, 50, 348–365. First published online in 2021. Evidence on response processes.