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#1: Josh Greifer (joshgreifer) on Apr 5, 2010 [HINT] [SPOILER]

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This is kind of going too far. I'm not a fan of "domino" logic. Sorry.

great puzzle - this is what this web site should be for - hard puzzles, not those colourful crappy things with too many spaces filled in that there is no skill needed - this is a PUZZZZZZZZLE site, not a picture site.

Me encanto, la verdad es que aplicando simple logica se resuelve y ya entendiendo el sentido se va resolviendo solo, felicidades!

That part of my brain is just not working today. Instead of extended edge logic, I tried to imagine how it would fit together, like making a puzzle out of shapes. It was fun to see it solve that way, but it was not true logic, as I did not do any sort of "if, then" process, just totally visual.

Found to have a unique solution by jan.

Found to be logically solvable by jan.

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I also notice that this puzzle is symmetric about a diagonal, but it's not immediately obvious to me that that would help us solve it, if we were willing to use symmetry as a solution technique, say if we knew a priori that the solution is unique. Is diagonal symmetry of any use at all?

Jan, I'm glad you appreciated this puzzle. Of course you can use it, I'd be flattered. This ability for humans to be able to do "..and so on..." -- i.e. inductive -- reasoning while most computer solvers can't is the reason why I created these puzzles. I like to show that people are still better than computers at certain problems -- and to stimulate programmers to create smarter programs. I'm slightly annoyed by brute-force game players and solver programs -- I've written a PBN solver myself too, which is nothing special -- just a big dumb backtracker (pretty fast though)

BTW I deliberately increased the size of some of these "domino logic" puzzles just to break the 1 second solve time of your checker!

I was first attracted to this site by your very interesting "Advanced Solving Techniques" page, and the different "logics" you identified there. This more humanistic way of approaching problems and puzzles and games has reaped rich rewards in a champion Gomoku playing program, where the language and terminology of expert Gomoku players has actually been coded into the program.

If I wanted to try and code inductive reasoning into a PBN solver I wouldn't know where to start really. I'd be very impressed if someone did it.


As to the holistic side, I agree it's also very hard to get a computer to do, but in this puzzle's case it's rather like the "summing" logic you describe in your Advanced Solving Techniques page.

The "colouring" techniques that Golomb used to prove theories about polyominos, are programmable -- I'm thinking of the most famous and simple example of checking whether you can use 31 dominoes to cover an 8X8 square with two opposite corners missing. A simple chessboard colouring of the square makes the answer obvious.

Thanks.

If you're interested in my survey, it's here: http://webpbn.com/survey/

If you want test data for your solver, or want me to test it against the others, I'm happy to do so. It's getting to be a pretty competitive business though.

I actually did the comparison of different solvers on variously scaled versions of this puzzle and wrote it up.

It's here: http://webpbn.com/survey/dom.html

I think this is a fun thing to put up as a challenge to designers of solvers.

I enjoyed this one, because the "aha!" came fairly quickly. If I hadn't found the solution right away, I would probably hate this puzzle. ;)

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Here's a link to a PDF of an Australian research paper called "MDD Propogators with Explanation". On page 17 you'll see a picture of this puzzle. They can solve up to size 20, which is way better than I've seen anyone else do.

So this puzzle is now officially part of SCIENCE.

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Great puzzle! I'm still struggling to get beyond line logic and this one helped me a lot.

I'm sorry to say that I "intuited" the solution and solved in about a minute. This was obviously meant to be a fun and tricky solve but I just gave it a lucky guess.

I tried a "reductionist" approach. Row clues and column clues occur in repeating pairs (1; 3 1;) (1; 3 1), and likewise for the columns. So I suspected I could discard two adjacent rows and two adjacent columns from the middle of the puzzle, and make a smaller puzzle. I then repeat this reduction a few times. Instead of a 19x19 puzzle, by time I cut it down to 5x5 I could see what was going on.

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