3QUESTION 3 OF 3
Answer & explanation
The official answer, with Fermi’s reasoning step by step.
Answer & explanation
Official answer
129,000
rows
How to estimate it
Fermi’s official “Napkin math”
Try a round guess: 100,000 rows. The bottom row has 100,000 people and the top has 1, so the average row is about 50,000. How many is that? 100,000 × 50,000 is 5 billion, not enough, so try a bit taller.
- Guess 100,000 rows, average row 50,000
- ≈ 5 billion, too few
- Try 120,000 rows, average row 60,000
- ≈ 7.2 billion, close
- A little taller still
- ≈ 125,000 rows
Rounded assumptions may give a slightly different estimate. The official answer above is the game’s reference value.
Source calculation & reference
- World population, mid-2026 (UN World Population Prospects 2024)
- ≈ 8,300,700,000
- Rows 1 + 2 + 3 + ... + n = n(n+1) ÷ 2
- n(n+1) ≈ 16,601,000,000
- Solve for n
- ≈ 128,800 full rows
- ≈
- 129,000
Reference cited by Fermi: United Nations World Population Prospects 2024, mid-2026 world population estimate
How close was your guess?
Your comparison will appear here.
Compare by ratio: divide the larger number by the smaller one. The closer to 1×, the better.