Anti Champernowne
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The number above shows a concatenating of the natural numbers in ascending order. What is the 2 8 3 8 3 rd digit from the left (1 being the first) of the number above?
The answer is 3.
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4 solutions
the 28383rd term is second digit of 7373 and not of 6374 so check your calculations after dividing 25494 by 4 and getting 6373 u forgot to add the 999 whose sum of no of digits you have subtracted from the total no of digits when you add 999 to 6373 you get 7372 and thus the required answer is second digit of 7373 which is also 3 (is that a coincidence??? Well definitely not)
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I did it right, first you have to remove 1,2,3 digits numbers that's why i subtract 2889.
You are absolutely right I also solved the same way. Sunil Gupta is absolutely wrong.
I think it is the second digit of 7373. When you get 6373 R2 you are finding out how many numbers you need to go up (past 1000). If you don't believe me (and Arpit Singh) look at the following example:
What is the 12th digit of all 4 digit numbers? Well 12/4=3 so you need to go 3 numbers up from 1000 (including 1000) and you get 1002. Then, since there is no remainder, you don't need to go up any partial amounts of numbers, so you get 2. Listing out the numbers 100010011002, we can see this to be the case.
As for our problem 6373 numbers up from 1000 is 7372. Then you must go two numbers past that into the second digit of 7373.
Wrong, Arpit Singh is right
wow, brilliant solution, at first sight at the problem, I cannot think of a way to give the answer, I thought there's no solution. , but you made it. thank you. (:
The first
4
−
digit number is
1
0
0
0
, so the
6
3
7
3
r
d
4
−
digit number will be
7
3
7
2
.
The remainder then obtained is
2
, as you wrote, so the next four digits are
7
3
7
3
, returning the answer as
3
.
should be 7373^^ (and second term is indeed 3)
Arpit Singh is right
Python 2.7:
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in response to brock brown solution is not like this(if it is, your answer will have been one of the choices)
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It is one of the choices; the program outputs 3 , the 28383th digit of 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 . . .
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ya you are right i understad :)
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@Sunil Gupta – I am confused what is the actual solution? And answer?
pff I prefer javaa
Let's look at a solution involving the value of subsequent nos in the sequence. There are 9 singles, 90 doubles, 900 triples, 9999 quad digit nos and so on.The no of digits done so far is 9999+900+99+9=11007. 28383-11007=17376. Divide it by 4 to know the value of the no. Needed in the sequence to cover the gap.Add it to 9999 to get 14343, with last digit 3. BTW, such questions should actually be in a school level programming test
- The number of digits of the first 9999 numbers is: 9 + 90x2 + 900x3 + 9000x4 = 38889.
- We can deduct that our answer is in a 4-digit number, so we can subtract multiples of 4 to 38889 so as to get the closest number to 28383 38889 - 4x2000 = 30889 ; 30889 - 4x600 = 28489 ; 28489 - 4x25 = 28389 ; 28389 - 4x2 = 28381
- Now we sum: 2000+600+25+2=2627.
- So the 28381st digit number will be the last digit number of 9999-2627=7372.
- The next number will be 7373, so the 28383rd digit number is 3
single digit numbers- total number of digits = 9.
2 digit numbers- total number of digits = 2x90 =180.
3 digit numbers- total number of digits = 3x900 =2700.
sum of these = 9+180+2700=2889.
4 digit numbers- total number of digits = 4x9000 =36000.
hence the 28383 rd digit belongs to a four digit number.
28383-2889=25494.
the 25494th digit of all 4 digit number is required dividing 25494 by 4 gives a quotient of 6373 and a remainder of 2. Hence the 28383rd term is the second digit of 6374 which is 3.
hence answer is 3.