Near 10
10 must remain within easy reach...
Age
14 to 16
Challenge level
Problem
How many integers $n$ exist such that the difference between $\sqrt{n}$ and $10$ is less that $1$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $39$
$\sqrt {n}$ needs to be between $9$ and $11$
$\therefore n$ needs to be between $81$ and $121$
So $n= 82, 83, ... , 119, 120$
$\overbrace{\underbrace{1, 2, 3, ..., 80, 81}_{81\text{ numbers}}, 82, ..., 120}^{120\text{ numbers}}$
So $82, ..., 120$ is $120-81=39$ numbers.