Fermi estimate: total kernel count in a 10 kg sack of rice

Quick Overview

A classic estimation question for product manager interviews: estimate the number of rice grains in a 10 kg bag. It tests breaking a problem down through the mass or volume of a single grain, stating round-number assumptions, converting units correctly, and cross-checking the result with a second method.

Fermi estimate: total kernel count in a 10 kg sack of rice

Company: Google

Role: Product Manager

Category: Product / Decision Making

Difficulty: medium

Interview Round: Other

A bag of rice weighs 10 kg. Roughly how many individual grains are inside it? Walk through your estimate step by step. ```hint Shrink the problem Work out what one grain, or one small spoonful, contributes before you scale up to the whole bag. ``` ### Clarifying Questions - What kind of rice is it: long-grain, short-grain, or a cheap mix with many broken grains? - Is 10 kg the net weight of the rice, excluding the bag? - How precise should the answer be: the right order of magnitude, or something tighter? ### What a Strong Answer Covers - A clear equation linking the bag's mass to a grain count through the mass or volume of one grain - Round-number assumptions for grain size and density, justified from everyday experience - Correct unit conversions between kilograms, grams and milligrams, or between liters and cubic millimeters - A cross-check by a second, independent route, and an honest range around the answer - How rice variety, broken grains and moisture move the result, and a quick practical way to measure it ### Follow-up Questions - If you had a kitchen scale for one minute, how would you tighten the estimate? - How would the answer change for a long, slender rice versus a short, plump one? - How would you scale the same approach to estimate the grains of rice a large city eats in a day?

Overview: A classic estimation question for product manager interviews: estimate the number of rice grains in a 10 kg bag. It tests breaking a problem down through the mass or volume of a single grain, stating round-number assumptions, converting units correctly, and cross-checking the result with a second method.

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Google
Dec 9, 2024
mediumProduct ManagerOtherProduct / Decision Making
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A bag of rice weighs 10 kg. Roughly how many individual grains are inside it? Walk through your estimate step by step.

Clarifying Questions Guidance

  • What kind of rice is it: long-grain, short-grain, or a cheap mix with many broken grains?
  • Is 10 kg the net weight of the rice, excluding the bag?
  • How precise should the answer be: the right order of magnitude, or something tighter?

What a Strong Answer Covers Guidance

  • A clear equation linking the bag's mass to a grain count through the mass or volume of one grain
  • Round-number assumptions for grain size and density, justified from everyday experience
  • Correct unit conversions between kilograms, grams and milligrams, or between liters and cubic millimeters
  • A cross-check by a second, independent route, and an honest range around the answer
  • How rice variety, broken grains and moisture move the result, and a quick practical way to measure it

Follow-up Questions Guidance

  • If you had a kitchen scale for one minute, how would you tighten the estimate?
  • How would the answer change for a long, slender rice versus a short, plump one?
  • How would you scale the same approach to estimate the grains of rice a large city eats in a day?