Of course it's for US residents only - and needless to say that people who can solve this problem well stand to make a lot more money than 50k if they found a startup specializing in this type of data recovery.
The prize is measly but a fascinating problem, no?
My initial idea is to dump all the material into a large room-sized box. Fans would then blow the clippings into the air (like lottery balls or something) and stop to allow it to settle.
Next a high res camera scans the jumbled scene closely from above (using an X-Y plotter). Upload the images onto a server.
Repeat many times.
Then process the data. First, images of individual clippings are extracted from the raw images.
Finally, images of the original paper documents are assembled by statistical algorithms similar to those used by Craig Venter to map and sequence the human genome.