Calling all math geniuses-baffling question need help!?

Question

ok here is a question i need help with-
Suppose u write all natural nos. in the foll. order:
1234567891011................ then
What is the 2007th digit(not 2007th number)?
I think the answer is 5 but got it in a long method. Anyone know a short method or formula?
An entrance question for AIEEE or IIT-JEE in the magazine Mathematics Today.
pls help me i really need help

Answer 1

There is a formular for the Nth number you have to make a few adjust ments to the formular to be in touch with your answer:I am not va math wiz but I am sure a math wiz could do it

Answer 2

can not do a million, yet 2-30: 2. C 3. D 4. A 5. A 6. D 7. C 8. A 9. D 10. B 11. A 12. A 13. A 14. a fifteen. C sixteen. C 17. D 18. D 19. A 20. A 21. D 22. B 23. A 24. B 25. A 26. A 27. B 28. A 29. B 30. B

Answer 3

I used a reasoning similar to what InsertAdjective did, and arrived at the same answer - the 5 in 705. As I lay out the thinking below maybe somebody else can see the formula developing.

1 - 9 >>>>> single digit numbers -- total digits used = 9

from here on we start counting by lines of 10s
10 - 99 >>> 9 lines of double digit numbers
.....................20 digits each per 9 lines
.....................20*9 = 180 digits this sequence
-----------------total digits used so far = 189

100 - 999 >> will be triple digit numbers
.....................30 digits each per 900 lines
.....................30*900 = 2700 digits this sequence
WAIT!!! that's already way too many digits used, we only need 2007.
Sooo... 2007-189 = 1818 more digits needed.
1818 digits, at 30 digits per line - hmmm ???
1818 divided by 30 = 60.6 lines, which means the 2007th digit will be on the 60th line (of 10 numbers) after the line starting the triple digits, which was 100. The 6/10 of a line will be .6x30=18th character on that line, which is the last digit of the sixth numer on that line.
60 lines at 10 numbers each = 600
600 + starting point of 100 = 700
The sixth number of the sequence line starting with 700 is 705, making the 18th character on that line, and therefore the 2007th digit of the sequence (drum roll please) "5".

Sorry for making this so long and drawn out, but mom & dad, and my Grandfather always made me show my work, when doing math. How else can you see if you made a mistake? Dad and Grandpa were engineers, so the accuracy of calculations was always very important. Check, double-check, and rework the problem backwards to make sure your answer is right.

It's interesting to note that 4 of us who took on this math challenge so far are female. We can be good at math when we apply ourselves. This blonde ain't so dumb either, for what it's worth, I have a Mensa card in my wallet. ;-)

Answer 4

i got the 5 in 705 i explaine my method below but don't take this answer as being correct.

1-9 are the first 9 digits
10-99 are the next 180 digits (90*2) giving 189 digits
100-999 are the next 2700 digits (900*3) giving 2889
this means you have to go back 882 digits which is 294 numbers.

Answer 5

The "long" formula is relatively short in Lisp:

(aref
___(with-output-to-string (s)
______(loop as n from 1 to 1500
_________do (princ n s)))
___2006)

The answer it gives is 5.
The 2006 is because Lisp array indexes start with zero.

The underlines at the beginning of each line of the program are because Yahoo Answers would otherwise mangle it to make it unreadable.

The 1500 is just a rough estimate of how many numbers are needed to insure there will be at least 2007 digits.

Answer 6

Its 6, the in the sequence 706

Answer 7

It is 16, I think, but then again I'm still in Algebra. I have no clue I got this answer.