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Solve estimation and probability brainteasers
Brainteaser Questions
Answer the following independent brainteaser questions. Clearly state any assumptions you make for each problem.
- Tile a floor: A floor measures 15 ft × 20 ft. You plan to cover it with square tiles, each having an area of 1 square yard. Approximately how many tiles are needed?
- Doubling account: An account begins with $1000 and doubles its value every year. How much money will be in the account after 20 years?
- Estimate Earth–Moon distance: While looking at the Moon from a window, estimate the distance from your location to the Moon. Use reasonable "back-of-the-envelope" reasoning and clearly state your assumptions.
- Stones in a boat: A boat is floating in a lake with several stones inside it. If you throw these stones into the lake, does the lake's water level rise, fall, or stay the same? Explain your reasoning.
- Probability of even product: There are two identical boxes. Each box contains three cards labeled 1, 2, and 3 (one of each). You draw one card from each box uniformly at random. What is the probability that the product of the two numbers drawn is an even number?
- Uncompressed 1080p movies on a 2 TB drive: Approximately how many uncompressed 1080p movies can fit on a 2 TB hard drive? You must clearly state all assumptions made, such as frame rate, color depth (bytes per pixel), typical movie length, and the exact definition of a Terabyte (TB).
- Nested squares area: Three squares are concentrically nested, with each inner square formed by connecting the midpoints of the sides of the previous (outer) square. If the innermost square has an area of A, what is the area of the outermost square?
AI interview prep
Core dilemma
Demonstrating structured problem-solving, critical thinking, and the ability to make and justify reasonable assumptions under uncertainty, rather than just arriving at a correct answer. The core conflict is between speed/simplicity and rigor/precision in estimation.
Mid-level signals3
Senior signals3
Red flags4
2 tradeoffs and 2 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Solve estimation and probability brainteasers
Brainteaser Questions
Answer the following independent brainteaser questions. Clearly state any assumptions you make for each problem.
- Tile a floor: A floor measures 15 ft × 20 ft. You plan to cover it with square tiles, each having an area of 1 square yard. Approximately how many tiles are needed?
- Doubling account: An account begins with $1000 and doubles its value every year. How much money will be in the account after 20 years?
- Estimate Earth–Moon distance: While looking at the Moon from a window, estimate the distance from your location to the Moon. Use reasonable "back-of-the-envelope" reasoning and clearly state your assumptions.
- Stones in a boat: A boat is floating in a lake with several stones inside it. If you throw these stones into the lake, does the lake's water level rise, fall, or stay the same? Explain your reasoning.
- Probability of even product: There are two identical boxes. Each box contains three cards labeled 1, 2, and 3 (one of each). You draw one card from each box uniformly at random. What is the probability that the product of the two numbers drawn is an even number?
- Uncompressed 1080p movies on a 2 TB drive: Approximately how many uncompressed 1080p movies can fit on a 2 TB hard drive? You must clearly state all assumptions made, such as frame rate, color depth (bytes per pixel), typical movie length, and the exact definition of a Terabyte (TB).
- Nested squares area: Three squares are concentrically nested, with each inner square formed by connecting the midpoints of the sides of the previous (outer) square. If the innermost square has an area of A, what is the area of the outermost square?