Back-of-the-Envelope Count of Canada's Cows
Company: Google
Role: Product Manager
Category: Product / Decision Making
Difficulty: medium
Interview Round: Other
Estimate how many cows there are in Canada. Show how you break the problem down, label each assumption, and end with a figure, a range and how confident you are in it.
```hint Find an anchor
Start from something about Canada that you can estimate with more confidence than the herd itself, then work out how many animals that quantity requires or implies.
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### Clarifying Questions
- Does "cows" mean only dairy cows, all adult female cattle (dairy and beef), or every head of cattle, including calves, steers and bulls?
- Is the count a snapshot of animals alive on one day, or every animal that passes through Canadian farms during a year, including those slaughtered or exported?
- How precise does the answer need to be: an order of magnitude, or within a factor of two?
### What a Strong Answer Covers
- A settled definition of "cow" and of the count basis, one day or a whole year, before any arithmetic
- A top-line equation that links a quantity you can estimate to the number of animals under that definition
- Labeled, round assumptions, each with a one-line rationale grounded in how cattle are raised
- Correct, unit-consistent arithmetic that keeps every figure on the agreed count basis
- A sanity check from a second angle, a final range, and how the figure changes under the other definitions of "cow"
### Follow-up Questions
- Which single assumption moves your answer the most, and how would you tighten it?
- How would trade in milk, beef and live cattle affect your count, and what goes wrong if you ignore it?
- If the interviewer switched the count basis, from one day to a whole year or the reverse, how would your number change and why?
Overview: A classic estimation exercise asking roughly how many cows live in Canada. It tests defining what counts as a cow and over what period, anchoring the estimate on a quantity that can be sized with confidence, keeping the arithmetic consistent, and sanity-checking the figure.