Saturday, September 27, 2014

JMO - number

If P =1234567891011.............9989991000

Find the 1000th digit from the left



Answer:

number of one digit numbers = 9 - 1 + 1 = 9
number of  2 digit numbers = 99 - 10 + 1 = 90
total number of digits in the 2 digit numbers = 2 x 90 = 180

number of digits remaining for the 1000th digit = 1000 - (9 + 180) = 811

to establish the 3 digit number at the 1000th place we divide 811/3 = 270 (1/3)

therefore, the natural number where 1000th term will be located is  9+ 90 + 270 + 1 = 369

please note the fraction 1/3 above. It means the first number of a three digit number.

so, the 1000th term is 3693. The answer is 3.


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