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MCSP

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Very glad you enjoyed it!

For the ZK example, the math behind it is this: if there are m bordering regions and I am lying, you have a 1/m chance of catching me each time. Thus after k repetitions the chance you haven't caught me is (1-1/m)^k \approx e^{-k/m} which is extremely small for k sufficiently larger than m.

Now, you may rightfully say: hey that's still not a "proof," you could still be lying! There are two responses to this:

1. The probability can be made incredibly small, like smaller than the the chance, say, your computer got hit by a gamma ray burst that would flip bits from 0 to 1 (I really have no idea if this actually happens but people have said it to me).

2. It turns out it is mathematically impossible to get the zero knowledge property if you want true proofs (i.e., no probability of being wrong). So, there's a trade off: if you want zero knowledge, you have to accept some (small) failure probability

P.S. Adding an easter egg for coloring the larger graph is on the todo list :)