See here for basic rules on problem.

Input/Output Problem #1

Problem #7

Make an optimal machine that accepts sequences of integer digits 1-4 such that each triplet contains three different numbers. Accepted examples; 123124234, 231123. Rejected example; 122341

You do not need a route for failed sequences.

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    $\begingroup$ Welcome to Puzzling. Can you please tell the source of these 'puzzles'? Are these your homework? $\endgroup$ – ABcDexter Nov 14 '18 at 17:50

I think beemaad's solution is optimal if the solution has to be deterministic. However, since the rules state that we can have multiple possible transitions from a given state for the same input, we can get this one down to 9 states.

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  • $\begingroup$ Looks reasonable to me. $\endgroup$ – beemaad Nov 15 '18 at 12:04
  • $\begingroup$ Was what I was looking for +1 $\endgroup$ – Ben Franks Nov 15 '18 at 14:55

Assuming, the empty sequence gets accepted, this should work:

The machine can be simplified by accumulating the sequences 12 and 21, 13 and 31, etc. Input/Output

  • $\begingroup$ Nice answer +1. $\endgroup$ – Ben Franks Nov 14 '18 at 14:19
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    $\begingroup$ You're really into this beemaad :) $\endgroup$ – user52327 Nov 14 '18 at 14:19
  • $\begingroup$ Can you optimise this further? $\endgroup$ – Ben Franks Nov 15 '18 at 0:18

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