- #1
diana.hole
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Homework Statement
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.
Homework Equations
N/A
3. The Attempt at a Solution [/b
i know that the pigeon hole principle should be used but I am not quite sure how to apply it, or word the answer correctly.