ENHANCED_MENSAN_PROBLEM(N,J,K,L): 1. prisoners #1 & #2 agree on a protocol. 2. prisoner #2 leaves. 3. Warden chooses N-bit string. 4. prisoner #1 flips up to J bits. 5. prisoner #1 leaves. 6. Warden flips up to K bits in attempt to ruin it. 7. prisoner #2 re-enters, observes pattern, and deduces message from prisoner #1, which could have been up to L possible messages.
Anyone see how to solve that one (& good parameter sets N,J,K,L to suggest)?
--I suspect good parameter sets arise when there are binary error correcting codes with blocklength=N, odd Hamming distance=2J+1, and such that its "dual code" can be tiled by L disjoint translates of a code with Hamming distance=2K+1. But there is a good chance I'm confused. Anyhow this kind of combinatorial entity is more involved than just "a code" and tabulating good exemplars might be worthwhile.