Help with a particular type of hint...orange and red can only be paired with A or X?

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  • pat44
    Member
    • Sep 2025
    • 2

    #1

    Help with a particular type of hint...orange and red can only be paired with A or X?

    These come up all the time for me and I am just stumped. I've gone over the tutorials over and over.
    Which TYPE of logic issue is this?

    For example, in my puzzle the clue is "Of the OIL CREW team and the team that finished third, one uses orange paintballs and the other uses red paintballs"
    The hint says "If Oil Crew does not equal first, and orange and red can only be paired with either Oil Crew or third, then orange cannot be equal to first. Mark the highlighted cell as FALSE."

    Is this a Transitive Relationship?

    Truly in awe of how quickly people are able to solve these logic puzzles. I am getting better. But almost always get stumped on this type. THANKS in advance!
  • JoshGrams
    Member
    • Jul 2025
    • 2

    #2
    Yeah, that's the last slide on the Transitive Relationship set: that's a complicated one.

    This is probably easier to see if we look at just one half of that clue: "orange paintballs must be the Oil Crew or the team that finished third."

    So if orange is NOT third, it must be Oil Crew, and thus it must be in one of the other placements that's compatible with Oil Crew.

    In your case, you have Oil Crew marked as NOT first. So if orange were in first place, then it's not in third place, AND it can't be Oil Crew (because Oil Crew can't be in first place).

    Then you can treat the other half of the clue the same way (red can't be in first place because then it wouldn't be third AND it would give a contradiction if it were Oil Crew).

    Does that help?

    Once you understand the logic, to see them I'm looking at the row and column of the Oil Crew/third pairing: Xs there may be able to be transfered to the other side of the either-or.

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    • pat44
      Member
      • Sep 2025
      • 2

      #3
      I will continue to study this. I’m glad to hear it isn’t easy!

      Comment

      • JoshGrams
        Member
        • Jul 2025
        • 2

        #4
        Hmm. Consider this grid, maybe? Assume you have the Xs in the top left (names/ages) section, and a clue that says "The 12.0 foot long crocodile is either Darwin or the 20-year-old."

        I've marked the 12-foot crocodile as being Drake but you can see that that's invalid because then it's not Darwin, but the X at Drake/20 blocks it from being 20 years old.

        Similarly, the 12-foot crocodile couldn't be five years old (not 20, but Darwin is blocked by the other X).

        transitive-exclusion.png

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