A mystery hunt puzzle at a math contest?

As my previous post noted I was helping to organize a big competition for this weekend. That’s now happened. Major relief there. I still intend to get two Wednesday puzzles and a pack out this coming week.

Since this is a puzzle blog and not a math contest one, most of the rounds and problems are probably not of that much interest to you all (if I’m wrong about this, check here in a couple days). The exception is that one of the rounds which was unofficial and did not count for score was written to be sort of a hybrid between a math contest round and a mystery hunt style puzzle (although there’s no final answer word or anything). It ended up being way too hard and few teams picked up on any of the gimmicks, but that happens sometimes. Presuming you haven’t completely forgotten how to do math problems, you puzzle enthusiasts might fare better on it.

CHMMC 2012 Mixer Round (PDF)

(The name mixer round has to do with how we shuffled teams before giving it out and has nothing to do with solving the round itself.)

As noted above, there’s no final answer; once you’ve answered all 12 problems you’re done. Feel free to email me for answer checking or hints or whatever. Or just wait until I get back to posting my usual content.

(Edit on March 14th: We’ve now posted solutions to all the rounds of the competition, including this one.)

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9 Responses to “A mystery hunt puzzle at a math contest?”

  1. Murat Says:

    Great work! I wish they had such mystery hunt puzzles in Mathematical Olimpiads.

  2. Anonymous Says:

    Awesome. Love good ol’ math.

    Got certain lacking answers for Part 1, and was just about to ping you asking about it when the missing trick hit me. What a perfect introduction to the set.

    Thanks for the fun, as always!

  3. Bryce Herdt Says:

    I haven’t picked up on the disambiguation trick, and I don’t see an easy way to solve #4. Nudge?

    • MellowMelon Says:

      #4: Set up a recurrence relation to compute A and B for specific n until you get equal terms at some point.

      If disambiguation means what I think it does, there’s no trick; leave things ambiguous.

      • Bryce Herdt Says:

        Yes, recurrence was somehow not an instinct I had. And it was pretty easy.
        But by “disambiguation,” I mean figuring out which of two answers to take for 1a and 3a, which I assume has something to do with Part 2.

      • MellowMelon Says:

        In that case disambiguation did mean what I thought. But just 1 and 3?

      • Bryce Herdt Says:

        Then I read zpuzzles’s comment (mostly) and your answer.

        For 2, I saw “line BC” and thought “segment.” I missed the obvious answer for 4 and 5. In 6, I missed “in some order.” And also, I miscalculated one answer for 3.

        Okay, on to Part 2.

  4. zpuzzles Says:

    I’m not sure i have the trick right, so to make sure rot13′d is it that

    sbe rnpu ceboyrz gurer ner gjb nafjref, naq sbe rnpu nafjre, gurer ner gjb ceboyrzf gung unir gung nafjre. Sbe gur svefg cneg gur nafjref ner gjraglbar, gjraglgjb, gjraglfrira, mreb, rvtug, naq guerr


    • MellowMelon Says:

      That’s everything for part one. If you assume all the same things hold for part two (save for that specific list of six), there will be a unique solution.

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