An "impossible" mode could remove the sound played when selecting a note. Only those with perfect pitch would be able to get it though (or someone using another piano / keyboard for reference).
As a slight aside, I have always wondered (and never really found a conclusive answer) whether it's possible to train your absolute pitch perception. I have perfect pitch so I can't really test myself fairly (although it does make this puzzle very easy for me!). I've read on multiple occasions that exposure / training as a child is the best way to get it for life, and being musical as a kid might explain my ability to detect absolute pitch.