1. The problem statement, all variables and given/known data Consider this string of digits: A=03161011511417191111 It has two 0s, twelve 1s, zero 2s, and so on. We construct another string of digits, called B, as follows: write the number of zeros in A, followed by the number of 1s, followed by 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. We now repeat this procedure on B to get its derived string C, then get the derived string of C, and so on to produce a sequence of derived strings. A=03161011511417191111 B=21201111101 C=2720000000 D=7020000100 E=7110000100 F=6300000100 G=7101001000 H=6300000100 Notice that the last string equals a previous string so the sequence of derived strings will now repeat. show that if a string has less than 1000 digits, then its derived string has at most 29 digits. 2. Relevant equations N/A 3. The attempt at a solution[/b i know that the pigeon hole principle should be used but im not quite sure how to apply it, or word the answer correctly.