How do you create the number as mentioned below?

If we write all positive integers in a row (in our decimal system) we get 123456789101112131415161718192021222324252627282930

Write a function that returns the n-th digit of this gigantic number.

[Juull01]

I know how to solve the last part, but I really have no idea how to create that hugh number in Matlab.

Thanks in advance

[KSSV]

Type it manually?

Answer 1

[Massimo Zanetti]

Here it is

m=1:30;
n=12;
s=regexprep(num2str(m),' ','')
s(n)

[Juull01]

Thank so much for your help! I really appreciate it I worked on it for like 2 hours and couldn't get the answer.

[Massimo Zanetti]

If you like my answer, please accept it. :)

Answer 2

[Marc Jakobi]

I won't tell you how to do it since this sounds like homework, but here are some functions that may help you.

str2double() % convert string to double
num2str() % convert double to string

to combine two strings:

a = 'a';
b = 'b';
ab = [a, b];

returns

'ab'

and

ab(2)

returns

ab(2) = 'b'

Answer 3

[Star Strider]

Without using strings at all, this works strictly numerically:

M1 = repmat([0:9], 10, 1);
M2 = repmat([0:9]', 1, 10);
M3 = cat(3,M1, M2);
M4 = reshape(M3, [], 2);
M5 = reshape(M4', 1, []);
Out = [1:9 M5(21:end)]

Answer 4

[Walter Roberson]

For amusement, a Maple version of the general solution, using direct numeric calculations without creating the intermediate values.

H := proc (M)
  local min_numdig, contrib_from_min, leftover, dp1, base_number, dig, dig_offset;
  min_numdig := floor(((1/9)*ln(10)+LambertW((1/90)*ln(10)*(9*M-1)*10^(8/9)))/ln(10));
  dp1 := min_numdig+1;
  contrib_from_min := (1/90)*10^dp1*(9*min_numdig-1)+1/9;
  leftover := M-contrib_from_min;
  if leftover = 0
  then
    dig := "9"
  else
    base_number := 10^min_numdig-1+floor(leftover/dp1);
    dig_offset := `mod`(leftover, dp1);
    if dig_offset = 0
    then
      dig_offset := dp1
    else
      base_number := base_number+1
    end if;
    dig := sprintf("%d", base_number)[dig_offset]
  end if;
  dig
end proc;

Note: this fails on 0 due to both a Maple technicality and a logic bug. The mathematics of it is presented without proof.

No MATLAB version of this will be provided, as the question is obviously a homework question.