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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, 2018 at 17:50

2 Answers 2

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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.

enter image description here

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  • $\begingroup$ Looks reasonable to me. $\endgroup$
    – user53694
    Nov 15, 2018 at 12:04
  • $\begingroup$ Was what I was looking for +1 $\endgroup$
    – Ben Franks
    Nov 15, 2018 at 14:55
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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

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  • $\begingroup$ Nice answer +1. $\endgroup$
    – Ben Franks
    Nov 14, 2018 at 14:19
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    $\begingroup$ You're really into this beemaad :) $\endgroup$
    – user52327
    Nov 14, 2018 at 14:19
  • $\begingroup$ Can you optimise this further? $\endgroup$
    – Ben Franks
    Nov 15, 2018 at 0:18

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