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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.
How Many Squares?
Age 14 to 16
ShortChallenge 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.
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