For you math freaks out there, help!

[gunmnky]

Erm, I'm pretty sure the results are not into the billions. It's 4 faces in 12 possible locations. or 4^12. That leaves 16,777,216 combinations

[RandomThoughts]

Erm, I'm pretty sure the results are not into the billions. It's 4 faces in 12 possible locations. or 4^12. That leaves 16,777,216 combinations

Sorry, but that's obviously wrong.

Even if we limit ourself to a single pattern like this:



We can still put 12 different tiles in the first slot, any of the remaining 11 tiles in the second slot, etc. That's where the 12*11*10*9*8*7*6*5*4*3*2*1 part of my formula comes from, which totals the billions already. After that, each single tile can be placed facing two different directions. That's x2 for every single tile again, or 2x2x2x2x2x2x2x2x2x2x2x2 or 2^12 or 4096.

After that come the different tile layouts, which are more difficult to calculate, but I feel pretty confident about the number 280.

SSo. I'm sorry, but I don't think your calculation is anywhere near complete.

[Sir_Turalyon]

<sane mathemathican voice>
It's two faces (a long face can't be interchanged with a short one) per tile in 12 slots, all right, times 12! ways to assign tiles into their slots (if tile goes from center into a corner ot table it becomes a different table!), times ~1104 different ways of covering table with tiles (arranging the slots themselves; tiles long edges may go all paralel to tables long edge, or all perpendicular, or in many more combinations).

So right, it's ~1104 * 12! * 2^12 , or ~1104 * 479.001.600 * 1024 * 4, or ~1104 * 1961990553600 or ~2.166.037.571.174.400 tables.

My previous estimation was way off, I blame sleep deprivation One could start going through all combinations by moment of Big Bang, take whole 4 long minutes to set up each new table combination and still be done about present moment. Give or take 40 millenia .

[Sami]

I hope you're all also ruling out table layouts which are identical to others when rotated. For example:

67890
12345

is the same as this:

54321
09876

Because in this game we pick which side of the table we fight on

[madd0ct0r]

that's not too bad...

if you lay the board out as a square, then for any particualr layout, there's 4 possible rotations. (there's possibly also a another four rotations of the mirror, but that's only true if each tile is perfectly reflectable, which is unlikely).

so to eliminate the rotations, just divide the final number by four.
(If you lay the tiles out as a rectangle, then divide by 2 instead.)

This (and the previous work) seems to assume you lay the tiles out in a single recangualr array. If you're prepared for a non-rectangualr board with irregular edges...
the number of possible combinations just went up by a few zeros.

[Johnmclane]

OK , let the mathproblem be a sleeping dog, but I promised to show the actual board to some of the posters here so here goes:

http://www.warseer.com/forums/showth...iallike)/page3

Take care
John