Multiple states can have the same output. THe same output is not enough to make a state unique. The things that make a state unique are the output AND how you reach that state and where that state can send you to. You have two states that output zero, but one state continues to the state that outputs 1, and the other state continues to a state that outputs 3. Therefore you have to unique states that output zero.When the first state is 0 which way the counter will count to 1 or to 3 ?
Counters have outputs. If you built a counter from states that output nothing you have no outputs so you have no counter. Plus the counter has to accept some input to know when to count, like a clock input.It's forbidden to use inputs or outputs for that question unfortunately. Do you have any other ideas?