What's really throwing me at the moment is the idea that phase-shift keying is on the right track, but the puzzle does not require being good at math or having a computer.

Representing digital information using sinusoidal waveforms seems to beg for math skills or a computer. Then again, we appear to have binary, so unless the answer is a waveform...

Or, what we have is a digital sampling of a waveform...but that's still math.

Clearly I've derailed somewhere.