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Question $6$

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The incomplete finite state machine below is meant to accept all strings of $0$ and $1$ where the $0\text{'}$s occur in consecutive groups of multiples of $3,$ i$.$e$.$ all the $0\text{'}$s are in groups of $3n.$ Examples include $110001000000$ and $000$ and $1110001100000011.$

Below the diagram is a list of numbers $0$;$1$ and $0,1.$ Complete the FSM by dragging the $0$ or $1$ or $0,1$ into the correct places on the diagram. Note that you can drag $0$ or $1$ or $0,1,0,1$ on an edge means that reading $0$ or $1$ will transition $($move$)$ to the new state.

Not all numbers need to be used, and you may use a number more than once.

$1$

$0,1$

$?$