• LAVA Moderator: Shinji Ikari

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^ How the painters doing?

OK, so there are 2^17 - 1 possible initial "starting colors" for the houses. Each acceptable coloring arrangement can be represented by a binary number. Each painter, when painting according to the rules, is essentially a function from one acceptable binary number to another. More precisely, each painter can be thought of as a permutation of the set of the 2^17 - 1 acceptable binary numbers.

My hunch is that these 17 "painter permutations" are elements of a group that is isomorphic to the integers mod 2^17 - 1 under addition. And more speciffically, each painter permutation corresponds to 2^17 - 1 - i, where i = 1, 2, 4...2^16. And hence, the composition of all painter permutations corresponds to (2^17 - 1 - 1) + (2^17 - 1 - 2) + ... + (2^17 - 1 - 2^16) = 16 * (2^17 -1) = 0 mod 2^17 -1.

And hence, the composition of all painter permutations is the identity function. So, after each has painted, the house colorings return to their initial state.

And the reason for my hunch is that I tabulated it for n = 2 and n = 3 (so, by golly, it should hold for n = 17).

Am I on the right track???
 
Had a spanish class, Creative writing/Poetry, and Religion in America. Im a great prose writer so this poetry class is great, learning how to write with a different kind of emotion. I like the religion one too, its quite interesting.
 
I'm Jewish and as alot of people hate Jews I like to get a better perspective as to why. And thanks RR, this is the best thread title Ive ever seen on BL (as Ive never been in one) ;).
 
Hmm. Being Jewish at a school which does not have a huge tuition cost is isolating. Is it the spoiled child stereotype you battle?

Do you wear your religion on your sleeve? Nothing wrong with it if you do, but that's a quick way to get negative attention. How do people find out you are Jewish?
 
It's not direct antisemitism I experiance the most though I have. I meant on a whole. People find out in like class as my last name is very Jewish, so sometimes I get looks nit alot though. Here it's not as bad but even on BL which most would consider liberal I have seen many people express this view as I know you have.
 
It's popular for anti-establishment, anti-captialism, anti-younameit people to extend toward antisemitism simply because it's what others are doing. Just try and shake it off; those are not people worth your time. In a way, it's like foreigners being anti-Americans. If you don't consider each person at face-value, then in the end you're just limiting yourself. Sans any higher up political movement - everyone at our level is just a person.
 
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