I can help you
But i am not sure about this part of the question
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Input
State 0 1
S1 S2 S3
S2 S2 S3
S3 S3 S1
Output Table
Input
State 0 1
S1 0 0
S2 1 0
S3 0 1
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Can you post more preciously they way you got it?
But some of your questions can be answered now.
1. how many inputs there should be?
Your question itself tells one input and one output. So there should only one input. The question is to design sequential circuit so clock must be applied. But this will not count as an input.
State table is a way to represent the state machine. It tells you for all possible inputs, how the state transition should happen. A hypothesis example.
input -----current_state ---- next_state
1 ------------ S3 --------------- S1
1 ------------ S1 --------------- S2
0 ------------ S2 --------------- S3
in above table when input is '1' if the current state is S3 then it should go to S1, (OR) if current state is S1 then it should go to S2. If input is '0' , if current state is S2 then it should go to S3.
From your question, in your state machine there must be three state S1,S2 and S3.