Locate the Digits!

Number Theory Level 4

$\large 1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9\ 10\ 11\ 12\ 13\ 14\ 15\ 16 \ldots$

All positive integers starting from $1$ are written in the order as of above as a single number. Find the digit appearing in the $206788^{th}$ position.

Also try this problem: Delete the Digits!

2 4 3 8 5 7 6 9

2 solutions

Rwit Panda
Sep 24, 2015

We can easily find that the 38889th term is 9 after which we move to the set of 5-digit numbers. Then we have 167899 terms left. We divide by 5 and get quotient 33579 and remainder 4. So the answer is 4th digit of 43579 which is 7.

We have to find 33579th 5 digit integer and 33579.

Kushagra Sahni - 5 years, 8 months ago

I mean the answer is 4th digit of 33579.

Rwit Panda - 5 years, 8 months ago

Okay, but actually we need to find 33580th 5 digit number which is 43579 and its 4th digit is 7 so answer is 7.

Kushagra Sahni - 5 years, 8 months ago

Ya you are right dude. Silly mistake. But tnx!!!

Rwit Panda - 5 years, 8 months ago

Jesse Nieminen
Sep 23, 2015

Number of n digit numbers is 9n * 10^(n-1).

206788 = 1 * 9 + 2 * 90 + 3 * 900 + 4 * 9000 + 167899

167899 < 5 * 90000, so 206788th digit is in a 5 digit number.

167899 = 5 * 33579 + 4

33580th 5 digit number is 43579 and 4th digit of it is $\boxed{7}$ .

Locate the Digits!

Also try this problem: Delete the Digits!

2 solutions

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