Question

How many positive integers less than 1020 have all their digits the same?

Answer 1

\[10^{20}\]

Answer 2

NOT 1020

Answer 3

Here is a hint 1 + 0+ 2 + 0= 3

Answer 4

can you find the answer if it were \(10^1\) or \(10^2\) or \(10^3\)?

Answer 5

you have to break this question down into smaller parts
1- How many one digit positive integers have all digits same (the answer is 9 obviously)
2- How many two digit positive integers have all digits same (well, the answer is 9 again)
3- How many three digit positive integers have all digits same (you guessed correct, 9 again)
4- How many four digit positive integers less than 1020 have all digits same (hmmmm, this sounds tough but the answer is 0)
5- Lets add all previous results and see what we get 9+9+9= ...
You can find the answer on your own ;)

Answer 6

now i realised the number we are looking for is \[10^{20}\]

again the answer is pretty simple as broken down above... each power of 10 bears 9 positive integers that have all the digits the same
so since there is 9 positive integers will all digits same in each power then we just multiply 9 by the power of ten we are looking for

so its 9*20=180

Answer 7

Yes that is correct, that method is a little long ,but its correct