Large Numbers Revisited (for Jean-Michel) « Next Oldest | Next Newest »

 ▼ Chuck Senior Member Posts: 320 Threads: 59 Joined: Dec 2006 01-09-2008, 08:07 PM Correct me if I'm wrong: There are : 256! (256 pieces) x 4^256 (each square piece can be put in 4 different positions) / 4 (the final solution can rotate in 4 different orientations, but remains one single) = 2,875 x 10^660 (!) solutions ```Hi Jean-Michel. My calculation would be like this: Corners: 4! remaining edge pieces: 56! interior pieces: 196! and only the interior 196 can be rotated for: 4^196 Divide by 4 for rotations gives: 4! 56! 196! 4^196 / 4 = 2.186011490004601*10^559 possibilities Yikes!!!! IBM's Big Blue can operate at little over 1 pitaFLOPS (1x10^15 floating points operations per second). Supposing it could operate continuously, it would only take about 6.931796962216517*10^536 years to run through all the calculations. I think I'll go buy a lottery ticket with a 1-in-a-billion chances to win (virtually infinitely more likely to win!). I wonder how many people purchased the game in hopes to win \$2,000,000.``` CHUCK Edited: 9 Jan 2008, 8:10 p.m. ▼ Don Shepherd Posting Freak Posts: 1,392 Threads: 142 Joined: Jun 2007 01-09-2008, 10:58 PM Go here for a discussion of the possible combinations. Yes, I bought it (\$50 bucks!). I just finished entering the edge patterns for the pieces (256*4). I don't expect to win the \$2 million, but I am looking forward to devising a clever non-brute-force algorithm for solving it. ▼ Chuck Senior Member Posts: 320 Threads: 59 Joined: Dec 2006 01-10-2008, 12:13 AM Thanks Don for the link my magnitude 559 is fairly close to the discussed 557 magnitude. I didn't realize there was a starter piece, so I can see how my 559 is a little high. I played their online 4x4 version, and solve it in about 1 min 20 secs. My 15-year old puzzle solving son wants me to get Eternity II. You never know, maybe he's got some unique hidden talent. :) CHUCK ▼ Don Shepherd Posting Freak Posts: 1,392 Threads: 142 Joined: Jun 2007 01-10-2008, 08:35 AM Hey Chuck, if you son expressed interest in this puzzle, I say go for it. I think it is more likely this puzzle will be solved by a kid with a special talent than a team of computer geeks. I tried the online 4x4 version too. I played with it for about 5 minutes, thought I had it solved but then the last piece did not fit. So I assumed it was real hard. So I challenged my 8th graders that, if any of them could solve it, I would give them all the money in my wallet (\$5). Sure enough, TWO of them solved it in about 5 minutes! Sometimes teachers learn lessons! Jean-Michel Member Posts: 191 Threads: 41 Joined: Jun 2007 01-10-2008, 07:21 AM Hello Chuck, In fact, I haven't seen the Eternity II puzzle. (That doesn't interest me much, I prefer considering the proabilities).I've just heard about it. I thought previously that all the 256 pieces were position insensitive. By reading what you wrote, then it seems that there are 4 specific pieces for the corners, 56 other specific pieces for the borders, and 196 internal pieces? This make a slight difference in the number of combinations, but does not increase in a sensible maneer the probability to became rich by solving this puzzle! Too bad :( Anyway, thank you for your post. Regards. J.-M.

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