Problem 15 · 2020 Math Kangaroo
Stretch
Number Theory
place-value
A certain number has 2020 digits. At most, how many digits can the square of that number have?
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Answer: E — 4040
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Hint 1 of 2
A '2020 number' means a number with 2020 digits.
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Hint 2 of 2
How many digits can the square of a 2020-digit number have?
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Approach: bound the size of the square
- A 2020-digit number N satisfies N < 10^2020.
- Then N² < 10^4040, so N² has at most 4040 digits.
- That maximum is reachable, so the answer is 4040.
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