Thanks for the feedback! As hcs suggests, this is part of the physical post-it assumption. I'll think about ways to make it more clear -- adding an FAQ is a good idea :)

All that's missing is more info in the answer to this question:

> Question: How do you do this in the digital world, without post-it notes?

Answer:

"When I give you a map labelled with numbers for each region, the numbers are the "post-it notes", "covering" the list of factors (which encodes a color). You can't see the primes factors inside them, because, even though generating an multiplying large primes is easy for computers, factoring numbers is much, much harder.)"

I think if, when the player checks "reply the demo, with numbers", you move the game down to where the prime number discussion is, it's easier to understand.

Also, note that the digital versionis better than the physical version. In the physical version, you can't stop me from removing extra notes. (A better example might be to put each color in a locked box, each with a different lock/key.) In the digital version, the factor lists are the "keys".

Thanks for the response, this and the rest of the comments here helped it finally click for me. I'm "recreationally" familiar with ZKPs, and always found the example of "video recording of alibaba" the most disappointing explanation, and the "I'm not color blind" demonstration the easiest to understand.

This demo was fun, and cool, and short (a undervalued virtue!). Awesome work. Thanks.

You do need to prove that you have assigned the colors before the choice of what to reveal is made, I think. Physically this is guaranteed by the presence of the colors under the post-its (barring dynamic e-paper or something).

I'm not sure how it works with the example of the primes, I lost the link to the later pages of the game so I can't read over it again, but I think it's guaranteed because there's just one number encoding all the assignments and you just get to unlock a single pair with the key given in response to your choice. There's an assumption that there isn't enough information in the key to fake any response, it has to reveal something that was already in there.

You're exactly right. The definition via primes ensures there is only one color consistent with each number (formally, this is called a perfectly binding commitment scheme). Also, here's the link if you want to go back: rahulilango.com/coloring/zk

Thanks! And this is a great exercise, thanks for sharing it.