Large Numbers Revisited (for Jean-Michel)



#6


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.


#7

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.


#8

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


#9

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!

#10

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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