Good challenges for a crypto competition for teenagers
Perhaps you could do something with Visual Cryptography.
Maybe something like:


Gather a few low-resolution images (symbols or short text phrases), perhaps a few more images than you have kids
Use visual cryptography to split each image into 2 random-looking images, and print each random-looking image on its own piece of transparency paper
Shuffle the pile of transparency papers
somehow let the kids find matching pairs of transparencies that show the original symbol or phrase.


Is there some way to let kids produce Visual Cryptography image-pairs "by hand", without a computer?

Links and further reading:


"What is Visual Cryptography"
online visual cryptography generator
"Visual Cryptography Kit"
visual cryptography example
"Visual Cryptography and Bit-Plane Complexity Segmentation"
XOR with polarized film