# What is the 28383th digit from the left (1 being the first) of the number 1234567891011121314...?

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1234567891011121314...

The number above shows a concatenating of the natural numbers in ascending order. What is the 28383th digit from the left (1 being the first) of the number above?

posted Jul 15, 2016

The series is in the below format -

1,2,3,4,5,6,.........10,11,12,..........,100,101,102,103,.........,1000,1001,1002,........

So,
one digit numbers( 1 to 9) - 9 => Total digits - 9 X 1 = 9
two digit numbers(10 to 99) - 90 => Total digits - 90 X 2 = 180
three digit numbers (100 to 999) - 900 => Total digits - 900 X 3 = 2700
four digit numbers (1000 to 9999) - 9000 => Total digits - 9000 X 4 = 36000
etc

Now hopping over the 9 + 180 + 2700 = 2889 digits the 4 digit numbers start in the sequence.
We have to go another 28383 - 2889 = 25494 digits. Since all the digits are four digit numbers (1000, 1001 etc) now, we divide 25494 by 4 we get 6373 and a remainder of 2.

So, our number is 6373 rd 4 digit number that is 999 + 6373 = 7372. After this we have to go another 2 digits to cover up the remainder. The next 2 digits are 7 and 3.

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