Question

Show that if a string has less than 1000 digits, then it's derived string has at most 29 digits.

Answer 1

what is a derived string?

Answer 2

I think ....
The derived string of a string is the string formed by the number of each of the digits \[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\] in the string.

For a string with less than 1000 digits, it is not..

Answer 3

well,this is a maths challenge question. it says for examples: consider this string of digits: A= 03161011511417191111. it has two 0, twelve 1s, zero 2s and so on.. W construct , another string of digits, called B, as follows" write the number of 2s and so on until we write the number of 9s thus B= 21201111101 string B is called the derived string of A, now we repeat this procedure on B to get it's derived string C, then get the derived string of C and so on to produce a sequence off derived strings.
A= 03161011511417191111
B= 21201111101
C= 2720000000
Notice that the last string equals a previous string so the sequence of derived strings will now repeat.

Answer 4

eg 10947576432 the derived string is 111121201 because there are 1 zeros 1 ones 1 twos 1 threes 2 fours and so on.

Answer 5

Since the original string has less than 1000 digits, there exists some digit d in
{0,1,2,3,4,5,6,7,8,9} that occurs less than 100 times (or else there would clearly be at least 100*10 = 1000 digits). This digit d therefore results in at most 2 digits in the derived string. Clearly the other 9 different digits, besides digit d, each occur less than 1000 times in the original string and therefore each result in at most 3 digits in the derived string.
Therefore, the derived string must have at most 3(9) + 2 = 29 digits.

Answer 6

what does that mean ?? I'm so confused. like what numbers do i put?