Find the 2014th digit

Number Theory Level 3

Let x = 0.12345678910111213 ⋯ 989999 x=0.12345678910111213\cdots989999 where the digits are obtained by writing the integers 1 through 999 in order .Then the 2014th digit to the right of the decimal point is


The answer is 7.

Vinayak Bansal by Vinayak Bansal , 17, India

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1 solution

X X
May 23, 2018

From 1 to 9,there are 9 9 digits.From 10 to 99 there are 90 × 2 90\times2 digits. 2014 − 9 − 2 × 90 = 1825 = 608 × 3 + 1 , 608 + 99 = 707 2014-9-2\times90=1825=608\times3+1,608+99=707 .So the 201 4 t h 2014^{th} digit is ⋯ 706707 7 08 ⋯ \cdots706707{\color{#D61F06}7}08\cdots

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Thank you for the solution !

Vinayak Bansal - 3 years ago

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Maybe next time you can use 2018 instead of 2014

X X - 3 years ago

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