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Tuesday, February 28, 2012

Quartzic: great free iphone ipad puzzle app

The object of Quartzic is to color the map (squares and rectangles) with only 4 colors such that, no 2 adjacent countries have the same color. This is based on a classic math theorem, which may or may not have been proved, I'm not sure.

There are 60 puzzles. Some puzzle levels require using blue or red a limited number of times; this complicates things! I am stuck on level 15. Without a doubt, this a challenging, fun game and is one of the best puzzle apps of 2012! Martin Roberts is the author - excellent job!


Bo said...

Long-time follower, commenting for the first time. :)

I think the color theorem is accepted as proven now. The problem is or was that it wasn't proven in the old-fashion way, utilizing classical ways of thought like induction etc., instead it was obtained by a thorough computer search.

Martin Roberts said...

Hi Tom,
Thanks for the positive review. Really appreciate it.

I agree with Bo, that since the original computer-based proof in 1976, there have been two more proofs more elegant than the original, but both still computer-based. With our growing power and usage of computing, these proofs have become virtually universally accepted, but everyone still quietly hopes that one day someone will provide an elegant traditional proof!

If you (or any of your readers) get stuck for too long, just email me via the email link in the app, and I'm happy to provide hints for any particular level. ;)

thanks again,

Simon Strange said...

Just a comment - the game is $1, not free! I know pricings change at a moment's notice, but I felt just a bit misled.

Tom Cutrofello said...

Thanks for the feedback everybody. If you find any worthy puzzle apps that I have not reviewed, let me know. Right now there are over 250 new puzzle apps per week. I'm trying to find all the gems, but I'm sure that I'm overlooking some.

Bo said...

@Martin Roberts

That must be fun, designing levels. Could you share some thoughts on that? I imagine you look for a particular graph and then its geometrical representation. Is there some relation between the level difficulty and some topological property like maximum vertex degree?

Martin Roberts said...


Yes. It is fun. It certainly appeals to the techie-geeky part of me!
One of the most interesting aspects that I have discovered on my journey is that there is only a weak connection between standard graph theory metrics (e.g. mnin/max vertex degree, avg/median degree, diameter, etc) and the difficulty of the particular level. This is probably because of the asymmetrical nature of the puzzle due to the color constraints (e.g. unlimited green and red, but only 2 red and 2 blue...)

So I have spent considerable time discovering and developing a robust and reliable method to determine the difficulty of a puzzle and it kind of mirrors the history of the 4-color theorem proof. That is, my method is part heavy-duty traditional graph theory aided with some heavy-duty computing power.

How far have you got? Did you find it too easy? Too hard?


Bo said...

Um, myself haven't installed it yet, that is purchased, having some problems with my iApparatus and payment.

Thank you for your thoughts.

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