intr to theatrical computer science

1-  Consider a TM tape containing a number in unary form (i.e., the number n is represented by a string of n 1’s).
Give a Turing machine that computes the function f(x) = x % 3 (i.e., that replaces the input number on the tape by its remainder when divided by 3.
Below, give a simple summary of the inputs associated with each state in your TM controller.

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2- Give a Turing machine that accepts the set of strings over {0.1} havng the form 0i1j with i _ j.
Below, give a simple summary of the inputs associated with each state in your TM controller.
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3- 
Describe the function computed by the following Turing machine. Assume the tape contains an input number in unary form (i.e., we represent the number n by a string of n 1’s).
for q3 I uploaded the picture

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