How many times is the number 9 used between 1 and 1000000?

Answer 1

If we throw 1000000 out of our calculations (this is okay because it doesn't have any nines in it) then we're left with all the numbers with 6 or less digits.

There are 10 choices for each digit. If the 100000's digit is 9, then there are 105=10000 ways to choose the remaining digits, so there are 10000 numbers that have 9 in the 100000s place. Similarly, there are 10000 numbers that have 9 in the 10000s place, 10000 numbers with 9 in the 1000s place, and so on. There are 6 different places 9 could be in, so the digit 9 is used 10000*6 or 60000 times.

Improved... well your missing a zero in your answer.... the total amount of 9's used should be 600 000 , not 60 000 because already in the hundred thousands digit 9 is being used 100 000 times becasue from 900 000- 999 999, the number nine is being used atleast

100 000 times so already your answer is wrong. And if you did you method corectly, it should be the same for every other digit, which means the answer will be that 9 will appear 600 000 times between 1 and 1 000 000. Correct me if im wrong, but im pretty sure that that is the answer.

(sources):http://www.cemc.uwaterloo.ca/contests/past_contests/2008/2008GaussSolution.pdf (question 25)

Answer 2

The number 9 is used 300,000 times between 1 and 1,000,000. This is because each digit from 0-9 appears an equal number of times in a uniform distribution.