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Show HN: I made a puzzle game that gently introduces my favorite math mysteries

rahulilango.com

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Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#121

Post by genewitch »

franciscop wrote: post #20

[spoiler alert] I knew that 4 colours sufficed for any arbitrary map from back in the day when I learned this, but still I found it VERY rewarding by attempting to draw a map that needed 5 colors, and how intuitive this demo was for getting a "feel" for a thing that I knew only theoretically! Like I needed an impossible geometry to fit, either an area that stretched to a zero-width path (which would becomes a point,…

there has to be a layman's explanation. I knew the easiest way to get four colors was to put a split square inside another split square "donut", but the reason you can't force 5 colors is that word "inside". There has to be a nice, tidy "verbal proof" that no matter what, one or more colors will be "trapped" inside at most 3 other colors.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#122

Post by genewitch »

gpnt wrote: post #117

> Warning: very difficult! Skip after trying a lot. I think "very difficult" is misleading here. It implies there is an answer if you try hard enough.

well, i knew there was no answer and i still tried for 15 minutes. I think that's the point!

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#123

Post by genewitch »

Halfwhit wrote: post #97
SamBam wrote: post #72

Earlier quoted context omitted.

I've always found what happens in the third dimension weird. A 0-dimensional space needs up to: 1 color. A 1-dimensional space needs up to: 2 colors. A 2-dimensional space needs up to: 4 colors. A 3-dimensional space needs up to: ∞ colors. I can easily picture why a 3D space has no limit to the number of colors (personally I always imagine color blocks hanging in space connected to every other color block by bendable…

Imagine the colours of a hypercube in 4-dimensional space!

A mantis shrimp told me, quote, "it's alright, i guess, if you're in to that sort of thing"

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#124

Post by namjh »

personjerry wrote: post #94

How does the zero-knowledge solution make sense? Can't you just cheat and show me two random different colors whenever I click two post-its?

In reality, the entire map should be sent first to the verifier (with colors hid behind the post-it) so if it was a bogus randomly colored map, you may find two adjacent points having same color if you try extremely many(think hundreds or thousands in the website's case) times. If you sufficiently try many times and fail to find the adjacent points, you will convince that the prover have the map which is correctly 3-colored.

Note that the entire map is sent again, shuffled its color each time after you choose the two points.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#125

Post by namjh »

Great work! I really enjoyed the interactivity. Actually I already was aware of the concept of zero-knowledge proof from the wonderful article by ZCash(which is a privacy-oriented cryptocurrency) core developer Matthew Green, worth to check it out: https://blog.cryptographyengineering.com/2014/11/27/zero-kno...

My two cents of the ZKP illustration is that directly using hashes are more likely to convince "computer-friendly" people to introduce the commitment scheme.

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#126

Post by genewitch »

teddarific wrote: post #75

Wow, this was a lot of fun. 3 was a lot harder than expected — a great exercise for anyone honestly. I'm a math nerd so this was cool visualized!

the easiest 3 is an equilateral triangle split in half with any shape containing it - for 4 split the container perpendicular to the split in the triangle.

|-/|\-|

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#127

Post by Guvante »

Fun fact, one of the reasons the four color problem is hard to prove is there isn't an algorithm that can color a map in four colors.

Well beyond effectively trivial ones where you try over and over again.

But the algorithm for coloring with five is pretty easy (relatively speaking still involves fun graph theory)

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#128

Post by waterproof »

genewitch wrote: post #121
franciscop wrote: post #20

[spoiler alert] I knew that 4 colours sufficed for any arbitrary map from back in the day when I learned this, but still I found it VERY rewarding by attempting to draw a map that needed 5 colors, and how intuitive this demo was for getting a "feel" for a thing that I knew only theoretically! Like I needed an impossible geometry to fit, either an area that stretched to a zero-width path (which would becomes a point,…

there has to be a layman's explanation. I knew the easiest way to get four colors was to put a split square inside another split square "donut", but the reason you can't force 5 colors is that word "inside". There has to be a nice, tidy "verbal proof" that no matter what, one or more colors will be "trapped" inside at most 3 other colors.

You would think. The easier, five-color theorem proof fits in a few paragraphs but the four-color theorem really resists a simple explanation. Even the simplified 1990s version of the proof (which came ~20 years after the original proof and 100 years after the 5CT proof) required enumeration of hundreds of individual cases.

https://en.m.wikipedia.org/wiki/Four_color_theorem

Re: Show HN: I made a puzzle game that gently introduces my favorite math mysteries

#129

Post by gavindean90 »

esquivalience wrote: post #32
zamadatix wrote: post #29

Loved the interactions and flow overall but I'm a bit lost on the zero knowledge proof example. I'm familiar with the concept but I don't follow how the example is one. E.g. "By repeating the process enough times, the probability that you never catch me becomes smaller than, say, getting struck by lightning" doesn't seem to show it's a proof? If I pick a hundred numbers it'll look like I just proved some black box fu…

I think the answer is that each time you reveal the colours, you observe that they are within the set of three colours illustrated at the beginning of the proof. Whichever you reveal, you never find a fourth colour. This confused me at first.

Reminds me of different colored swans
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