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Number Theory Level 2

If we write all the multiples of 6 side by side then a large number of number N will be formed as follows N=612182430....... The 1000th digit of this number N from left


The answer is 7.

Milun Moghe by Milun Moghe , 25, India

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2 solutions

Milun Moghe
Mar 20, 2014

HINT:

6 ⏟ , 12 , . . . . . , 96 ⏟ , 102 , . . . . . . . . . . , 996 ⏟ , . . . . . . . . \underbrace{6},\underbrace{12,.....,96},\underbrace{102,..........,996},....... . and so on

1 d i g i t ⏟ , 15 ∗ 2 d i g i t s ⏟ , 15 ∗ 3 d i g i t s ⏟ , . . . . . . . . . \underbrace{1digit},\underbrace{15*2digits},\underbrace{15*3digits},.........

Thus we can obtain the 1000th digit as 7

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Sunil Pradhan
Mar 31, 2014

[1 digit no = 3 ------ 1 No] [2 digit no = 12, 18, ... 96 ------ 15 No] [3 digit no = 1002, 1008, ... 9996 ------ 150 No] total digits = 1× 1 + 15× 2 + 150×3 = 481

digits remained = 1000 – 481 = 519 so 4 digit numbers required = 519/4 = 129 numbers + 3 digits of 130th number

T130 = 1002 + 129 × 6 = 1776 so 3rd digit of 4 digit number = 7 which is 1000th digit

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