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 0s 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 process 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=031611011511417191111
B=21201111101
C=2720000000
7020000100
7110000100
6300000100
71

Question

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 0s 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 process 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=031611011511417191111
B=21201111101
C=2720000000
7020000100
7110000100
6300000100
71

anonymous · Answer

my question is show that if a string has less than 1000 digits, then its derived string has at most 29 digits?? I've read two answers from the following forums and I am seriously confused because I do not understand what the pigeon holeprinciple is and I dont really get the explanations they arent really clear enough.... heres the links for the explanations: p://www.physicsforums.com/showthread.php?t=592018 http://openstudy.com/updates/4f757f2be4b0f07ddab19fc6