11 posts

## Eternity II

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• Is anybody working on solving Eternity II ?

Anyone caring to discuss the best approach to solve it?

Seba

• What stops someone from making a computer program that tries all combinations?

• (256 P 256) * 4 orientations per peice = 256!*4 = 3.43127e+507 possible combinations.

Nothing stops someone from trying all possible combinations, but you're not going to try all possible combinations in one lifetime.

• CannotResolveSymbol wrote:
﻿Nothing stops someone from trying all possible combinations, but you're not going to try all possible combinations in one lifetime.

If you have only 1 processor. I'm sure the Channel 9 community has more than 1 of it. This would be an excellent C9 community project/contest.

Who's going to buy the puzzle?

• ZippyV wrote:
﻿
 CannotResolveSymbol wrote: ﻿Nothing stops someone from trying all possible combinations, but you're not going to try all possible combinations in one lifetime.

If you have only 1 processor. I'm sure the Channel 9 community has more than 1 of it. This would be an excellent C9 community project/contest.

Who's going to buy the puzzle?

I still don't think you get the enormity of the problem...  it's 3.42*10^507 possible combinations.

Assuming you somehow figured out a way to evaluate a combination in one clock cycle, with a typical 2GHz processor, that's still going to take 1.71*10^498 seconds.  That's about 5.42*10^490 years, by my calculations.

If you had a CPU core for every person on earth dedicated to this problem (using this impossibly fast algorithm), it would still take you 8*10^480 years.

I'm sure there would be a way to solve this problem by computer, but brute-forcing it as you suggest is impossible.

• CannotResolveSymbol wrote:
I'm sure there would be a way to solve this problem by computer, but brute-forcing it as you suggest is impossible.

We're making progress on P=NP, so who's to say a trivial boardgame could be harder?

• CannotResolveSymbol, I think you're wrong. 256!*4 means that all the possible positions are used and for each combination ALL the pieces are rotated. Each position should be combined with an orientation => 256*4 possibilities per piece => (256*4)! = 5.418528796E+2639 total possibilities.

• TommyCarlier wrote:
CannotResolveSymbol, I think you're wrong. 256!*4 means that all the possible positions are used and for each combination ALL the pieces are rotated. Each position should be combined with an orientation => 256*4 possibilities per piece => (256*4)! = 5.418528796E+2639 total possibilities.

I was just giving a rough estimate.  If we really want to get into the math of it, (256*4)! would mean that there's also 256*4 spaces that you need to fill, so essentially you're treating it as if there's distinct pieces for each rotation and that all of those pieces would need to be placed.

More accurate would probably be (256!)*(4^256), eg:

Piece 1: 256 locations, 4 rotations
Piece 2: 255 locations, 4 rotations
...

256*4*255*4*...*2*4*1*4 = (256!)*(4^256) = 1.15*10^661

• You guys forgot that there are border and corner blocks, also there is a starter piece and 2 clue pieces . Wikipedia said:

A tighter upper bound to the possible number of configurations can be achieved by taking into account the fixed piece in the center and the restrictions set on the pieces on the edge: 1 × 4! × 56! × 195! × 4195, roughly 1.115 × 10557

• CannotResolveSymbol wrote:
﻿I'm sure there would be a way to solve this problem by computer, but brute-forcing it as you suggest is impossible.

I know, but still, my programm is running... go knows, I might get lucky

Seba

• sgomez wrote:
﻿
 CannotResolveSymbol wrote: ﻿I'm sure there would be a way to solve this problem by computer, but brute-forcing it as you suggest is impossible.

I know, but still, my programm is running... go knows, I might get lucky

Seba