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Comment by zeroonetwothree

> For example, it could be possible that, if we generated a random map in some way, 99% percent of the time, the three-color map coloring problem would be easy, but 1% of the time, it would be very difficult.

> This would still be NP-complete, but would make for a terrible cryptosystem - a scheme based on this problem would be easily broken 99% of the time!

I don’t think this explanation is great. We could just generate instances until we found the hard one and then use it. So the answer is more complex than just as written.

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