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I have a 4x3 cubic picture puzzle with 6 correct answers. Each piece in an inch^3 (l=b=h=inch=2.5cm). I can figure out the arrangements of this puzzle i.e. Each block in the puzzle can move in 24 ways so, arrangements in which each piece of the puzzle is in-situ is 24^12. The number of ways the pieces can be moved around in the puzzle is 12!. But 1/2 of the arrangements are mirror images. So, the total number of arrangements is 1/2*(24^12)*12!. Now, lets say each piece of the puzzle is scanned at 300dpi. Is that too much? Hence each piece would be a 300x300 matrix. For fun, if we were to assume it to be a black and white puzzle? What possible algorithms would be the go to solve the puzzle? And would it be worth the supercomputer's time?

The author has assumed 1 arrangement takes 1FLOP. He solved it by brute force and came to 40.5 days.

If we were to do the 300x300 matrix, the author is out by at least 90,000 times the answer.

The supercomputer operates at 415.5 PETAFLOPS.

The problem is illustrated in the video. Please help find flaws with his argument? What possible algorithms are there that can solve it faster! He makes rather funny assertions!

https://vimeo.com/658287281

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  • $\begingroup$ Why is the scanning relevant? A computer could easily work with abstract cubes having location and orientation. Further, it would seem that each cubic piece would have six 90 kpixel images associated with it, one per side. $\endgroup$
    – Eric Towers
    Dec 21, 2021 at 4:44
  • $\begingroup$ Scanning is irrelevant, I suppose the point was that there would be six 90kpixel images per cube.. btw .. have you watched the video? How you do solve this kind of puzzle? What algos could be used? $\endgroup$
    – Deep Lifeguard
    Dec 21, 2021 at 5:59
  • $\begingroup$ They're not mirror images, but 180 degree rotations. Also the argument does not take into account that you (or the computer) can tell when two cubes definitely don't match each other. It assumes that the computer can only tell if it is a correct solution once all cubes have been placed, that somehow it needs the last square to be filled before suddenly realising that the first two cubes that were placed don't match. The video is a piece of rubbish rhetoric. $\endgroup$
    – Jaap Scherphuis
    Dec 21, 2021 at 7:33
  • $\begingroup$ Hi Jaap, Unless I'm mistaken and according to wiki (en.wikipedia.org/wiki/Mirror_image) a mirror image is a 180 degree rotation. I suppose one cannot take into account all possible implementations of the problem, I am looking for a number of computations and time factor to solve the problem. You could formalize the argument by quantifying intelligence with information theory for the intellectual elite. The difference between a a system with intelligence and a system with no intelligence and a system with artificial intelligence and its current capabilities is the highlight $\endgroup$
    – Deep Lifeguard
    Dec 21, 2021 at 8:43
  • $\begingroup$ Absolutely, positively guarantee that I have not watched the video and that the current standards of this site require you to abstract and explain all relevant information to make your question freestanding (i.e., not reliant on a link that may or may not continue to work in the future). $\endgroup$
    – Eric Towers
    Dec 21, 2021 at 17:40

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