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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 by anonymous

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1 Answer

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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.

So our answer is 3.

answer Jul 27, 2016 by Indranil Datta



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