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 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.
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.
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].
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.
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.
Be careful! There's a whole world of mechanical puzzles out there, and it can get very expensive and start to take over your life.
Here's an assortment of links to places where you can buy interesting puzzles. This isn't exhaustive of course: it's just a few places that came to mind.
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.
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 :)
Fair point. The gradients are just to be pretty. We could make you a solid color version if you would like. Email orders@nervo.us and we can set up a custom order.
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).
We haven't actually run the thing to completion. We ran it for a couple days and then stopped after finding tens of thousands of solutions. Might explore again if we have time to improve the solver efficiency.
I did write a program to generate an exact cover. Thr output is a little over 5 megabyte when using a notation that list the indices of the positions that have a 1. I have not yet verified that it is correct. My solver found one solution so far and edtimates that the number of solutions is more than 10^50.
hi colordrops! the flummox coupon works in the shopping cart. often folks try to apply it in the gift card box in the checkout procedure. Let me know if you already placed and order and I can apply the coupon retroactively for you. If you would like to provide any more info on the checkout errors you can email me at orders@nervo.us
I'm somewhat ignorant about the search ranking implications of changing our domain. I bought the nervo.us domain much later and we've had the n-e-r-v-o-u-s.com domain since 2007.
