Guest Posted April 1, 2008 Report Share Posted April 1, 2008 Starting with 1 which number contains the 1000th consecutive digit? i.e 1 contains the first digit 2 contains the second digit ... 10 contains the 10th and 11th digits 11 contains the 12th and 13th digits ... what is the highest consecutive digit that 1000 contains? given a number n, what is the highest consecutive digit that it contains? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 1, 2008 Report Share Posted April 1, 2008 Which number contains the 1000th consecutive digit? 370. If my calculation is correct, the 1000th digit '3' in 370. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 1, 2008 Report Share Posted April 1, 2008 what is the highest consecutive digit that 1000 contains? 000-999 ==> 3*1000 digits = 3000 digits. But then we need to subtract the leading (one) zeros in 000-099 ==> 100 digits. 00-999 ==> 3000-100=2900 digits. We need to subtract the leading zeros in 00-09 ==> 10 digits. Then 0-999 ==> 2900-10=2890 digits. OP started from 1. Subtracting the first zero: 1-999 ==> 2890-1=2889 digits. So the last digit in 999 is the 2889th digit. 1000 contains 2890th, 2891st, 2992nd and 2993rd digits. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 1, 2008 Report Share Posted April 1, 2008 There are 9 single digit numbers, 90 2-digit numbers, 900 3-digit numbers, etc. ANSWER #1: 370 9*1 + 90*2 + x*3 = 1000 3x + 189 = 1000 3x = 811 x = 270.3333 Meaning that the 270th 3-digit number (369), will only have 999 total digits so far. The number 370 contains the 1000th digit (the number 3 is the 1000th) ANSWER #2: 2993 9*1+90*2+900*3 = 2889 1000 has 4 digits, so 2889+4 = 2993 ANSWER #3: Sigma notation for k going from 1 to d-1 of 9*d*10^(k-1) [end sigma notation] + d*(number - 10^(d-1)) where d is the number of digits the number has. Let d = number of digits the number has For x = 1 to d-1, calculate the sum of d*9*10^(x-1) for all values of x [calculates the total number of digits for smaller digit numbers] Then, add that to d*(number-10^(d-1)) [calculates the total of number of digits with that number and all other numbers smaller with the same digits] Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 2, 2008 Report Share Posted April 2, 2008 omg that is cazy Quote Link to comment Share on other sites More sharing options...
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Guest
Starting with 1 which number contains the 1000th consecutive digit?
i.e
1 contains the first digit
2 contains the second digit
...
10 contains the 10th and 11th digits
11 contains the 12th and 13th digits
...
what is the highest consecutive digit that 1000 contains?
given a number n, what is the highest consecutive digit that it contains?
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