What interesting audio can be synthesized with ifft
You can take a look at Photosounder. The idea behind is simple: Take an image as if it were an spectrogram and compute its IFFT, the result is  always interesting at least! It tends to work better with abstract images and geometric shapes, a great example is the video on the upper-right corner, "The sound of fractals".

I would never try to replicate a real instrument using this method, but you can encourage your fellows to try it as a challenge...