• LAVA Moderator: Shinji Ikari

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Did you know how many steps were on every single staircase within your college of choice? God damn, I probably had 70 numbers memorized. But I'd still count them each time to be sure.


I have a few weird habits like that

For example, whenever someone gives me a phone number or writes us a check, I'll either try to factor the check/phone number or tell the person, "hey, did you know your ch #1855 was the year Gauss died?"

"Who the fuck is Gauss???"

"nm"

And sometimes, I will adjust the pricing of a bid, so that the total comes out to something like $1,234.56
 
^that reminds me of that old puzzle, where you have to find the shortest distance an ant on the ceiling would have to travel to get to a point on a side wall.
 
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Let
x_0 = 0 = 00000000000000000

be the binary expression for when all houses are white. And let C be the third painter.

Then C(x_0) = 11011111111111111 = 2^17 - 1 - 2^14.

Then the isomorphic image of C in the integers mod 2^17 - 1 under addition* is 2^17 - 1 - 2^14, or simply C(x_0 = 0).

I can show that for all A & B in the {All 17 Painter Permutations}, AB(x) = BA(x).

I wonder if there is some way to show how {All 17 Painter Permutations} generates Z mod 2^17 - 1...

*So strange that addition should be the isomorphic function...
 
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