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I have a couple small ideas, even if they aren't very good.
Symmetric Music
Have the contestants write a piece for any keyboard instrument or two of the same monophonic instrument in which one voice is always a reflection of the other voice over a pivotal note. Anybody know what I mean by this? Try centering your attention on any D on the piano, and notice that the keys on either side are symmetrical so that C# corresponds to Eb, B corresponds to F, and so on.
Retrograde-inversion Duet Challenge
Mozart once wrote a piece called "Der Spiegel" for two violins which only consists of only one part. The second violinist plays from a copy of the same part, only physically turning the page upside-down. Have contestants write a piece for two of the same instrument such that the second part is actually the first part read upside-down.
These both would be very challenging for anyone, I'm not sure if things like these have actually been done before (except Der Spiegel).
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