You may also like

Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Rooted Via 10

How many of the numbers shown are greater than 10?

Largest Expression

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

How Many Squares?

Age 14 to 16 Short Challenge Level:

Answer: 68


The smallest integer with 4 digits is 1000, 1 more than 999 which only has 3 digits.

The largest integer with 4 digits is 9999, 1 less than 10 000 which has 5 digits.

10 000 = 100$^2$, so all integers whose squares have 4 digits must be less than 100.

30$^2$ = 900, 31$^2$ = 961 and 32$^2$ = 1024.

So all integers $n$ with 31$\lt n\le$99 have 4-digit squares.

So there are 99 $-$ 31 = 68 such numbers.



You can find more short problems, arranged by curriculum topic, in our short problems collection.