How to design and implement a sequence detector
Being kind of old myself, I expect you to study like #### too. :D 

One question may help clarify the circuit you need : how does it distinguish between 2 successive states that are the same? Or alternatively : Is there a separate clock signal, not mentioned above? If so, the basic pattern of the circuit may become clear.

Ask yourself :
how many states do you have?
how many bits are required to implement all these states?

You have already given each state a unique number : it will help to write those numbers out in binary as part of each state table.

Then treat each bit of that number separately : first create a Karnaugh map for the next state for bit 0. What are the input variables for that KMap?