Nice article, which also explains the mapping of the puzzle to an exact cover problem and how those can be solved with dangling links as in Knuth's Algorithm X.
Very interesting, but I have a hard time differentiating the colors. The gradients seem to be there for aesthetics only, but they confuse me to no end :)
Tangential, but does anyone know good places to find other physical puzzles like this? Also, recently there was an article on elastic knots I was hoping someone would productize into a novelty puzzle.
So many puzzles like this basically require you to brute-force the solution [0], which just isn’t all that fun. I’m glad the designers explicitly acknowledge they’re trying to avoid this, and really hope that their claim that this actually can be solved with logic holds true:
What if instead of doing the full colored puzzle, we find partial sets of tiles where there is only one unique solution? This adds enough constraints to the problem that it becomes feasible [without resorting to brute force].
Recently I designed a calendar puzzle with 10 tetris-like pieces. When you place all the puzzle pieces on the board, three squares/rhombuses are still open and together they form a date. Can you arrange the puzzle pieces in such a way that it shows todays date? See https://praxispuzzles.com/calendar_puzzle_rhombus Disclaimer: I sell these puzzles for a little more than the raw material.
You can arrange the puzzle pieces to make dates that don't exist, like Monday February 31. Actually there may be "impossible" dates, because I didn't check for them, but I think all combinations of days of the week, day of the month and month are possible.
You are right. This puzzle started my search into this type of puzzle. But in the end my puzzle is harder, because it also contains the day of the week and has the most "irregular" puzzle pieces possible.
It would be nice, if they could publish the exact cover. I have written some algorithm that can estimate the number of solutions to an exact cover base on the number of solutions it found and the size of the 'tree' that has been explored.
I could write a program myself to calculate the exact cover, but I guess, it will take me about a day to do so. It would not surprise me if the exact cover will be a few hundred mega bytes (when using one character per position).
I wrote a program to produce the exact cover for the puzzle and I did some experiments with my exact cover solver to find solutions and generate an estimate of the number of solutions. I am not very sure on the estimate. One run returned a number of 10^50 and another one (with a slightly different, but more successful search strategy) returned a number of 10^148.
The generated exact cover is about 5 megabytes using a notation the positions for the ones in the vector are listed.
The second run has now found about 200 solutions in about six hours, which is far less than the ten thousands that they have found [2].
I do not know of any other programs that can estimate the number of solutions of an exact cover.
21 comments
[ 3.9 ms ] story [ 52.5 ms ] threadTotally feeling like vibe-coding a web version of the game and plastering it with giant BUY THIS THING links that send people to the real thing.
https://en.wikipedia.org/wiki/Eternity_puzzle
I could write a program myself to calculate the exact cover, but I guess, it will take me about a day to do so. It would not surprise me if the exact cover will be a few hundred mega bytes (when using one character per position).
The generated exact cover is about 5 megabytes using a notation the positions for the ones in the vector are listed.
The second run has now found about 200 solutions in about six hours, which is far less than the ten thousands that they have found [2].
I do not know of any other programs that can estimate the number of solutions of an exact cover.
[1] https://www.iwriteiam.nl/D2510.html#16
[2] https://news.ycombinator.com/item?id=45559402