Till infinity, can't be determined

Logic Level 3

If we write down all positive multiples of 6, we get the sequence

6 , 12 , 18 , 24 , 30 , … 6, 12, 18, 24, 30, \ldots

What is the 1000th digit that is written down?

As an explicit example, the 5th digit that is written is 8, which came from 18.

This is not original.


The answer is 7.

Deepanshu Gupta by Deepanshu Gupta , 25, India

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4 solutions

William Lockhart
Sep 22, 2014

Sort of cheated. 

>>> n=""
>>> p=6
>>> while len(n)<1000:
        n+=str(p)
    p+=6
>>> n[999]
'7'
6 Helpful 0 Interesting 0 Brilliant 0 Confused

Oh Looping... Nice One..!! I know only Little about Looping which I had studied in my school days in my IP subject ..!!! AnyWay Good Work

Deepanshu Gupta - 6 years, 8 months ago

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Thank you :)

William Lockhart - 6 years, 8 months ago

I did brute force approach by COUNTING hell of experience any better solutions?

Priyanshu Pandey - 6 years, 8 months ago

Did the same! :P

Kartik Sharma - 6 years, 3 months ago
Akhilesh Bhandari
Sep 28, 2014

1 single digit multiple. There are 15 2 digit multiples ( form 12 to 96) , 150 3 digit multiples which makes a total of 481 digits. Remaining 519 digits will come from the 4 digit numbers . int(519/4) = 129 remainder = 3. So the 1000 digit will be the 3rd digit of the 130th 4 digit factor 130th number is 1774 . So the digit is 7

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Sazzad Bin azad
Sep 15, 2015

hard one but feeling happy after craking it

0 Helpful 0 Interesting 0 Brilliant 0 Confused

checking how many one,two,three,four digit multiples are there its easy to get the answer

0 Helpful 0 Interesting 0 Brilliant 0 Confused

can you explain bit more Please ???......Thanks

Deepanshu Gupta - 6 years, 8 months ago

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Gupta,

how many multiples of 6 are writen with one digit? just one: 6 (1 digit) how many multiples are writen with 2 digits? 15 numbers (15 x 2 = 30 digits) how many multiples with 3 digits? 150 numbers (150 x 3 = 450 digits) how many multiples with 4 digits?1500 numbers (1500 x 4 = 6000 digits).

So, until 996 you have 481 digits (1+30+450). Find the others between 1002 and 9996

Claudio Felipe - 6 years, 8 months ago

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