How many perfect cubes lie between $100$ and $1000$?

How many perfect cubes lie between $100$ and $1000$?
  1. $5$
  2. $4$
  3. $6$
  4. $7$

Solution

$5^{3}=125,\ 6^{3}=216,\ 7^{3}=343,\ 8^{3}=512,\ 9^{3}=729$ — five cubes.

Asked in: IMO

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