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[Ultima Ratio Regum]

Hello everyone! I'm better known on this forum for a different (hobbyist) project, but in my working hours I've been building something else. Alongside Professor Simon Colton (http://ccg.doc.gold.ac.uk/simoncolton/) of the Computational Creativity Group (http://ccg.doc.gold.ac.uk/) at Goldsmiths College and an artificial intelligence known as the HR system (http://www.doc.ic.ac.uk/~sgc/hr/), we've been developing a new kind of paper puzzle game. We're calling it Donatsu!

The HR system is a piece of software that automatically creates mathematical concepts and discovers conjectures about them. The system is now capable of generating and testing the solvability of puzzles within wide constraints, and we’ve developed a set of puzzles we’re calling Donatsu (transliterated Japanese for “Doughnut”). These involve the player following a loop (or various other loop-like designs) attempting to get a series of numbers to reach particular totals through adding mathematical operators (+, -, /, and x).

I've pasted in below four of the many permutations we've developed - Uninatsu (the most basic), Chromanatsu, Maxinatsu, and Hexanatsu (the most complex) - alongside appropriate instructions. You can also download to print off a paper version, since these are paper puzzles, after all! Our long-term goal is to develop and refine these to the point that we can potentially get some published in newspapers.

Seeing as these are designed to be done with pen and paper, you can download a PDF of all the puzzles here: http://www.ultimaratioregum.co.uk/game/download/donatsu-v1/?wpdmdl=6391

So: we'd love to get your feedback! Aside from the obvious - are these fun and interesting to solve - we'd also like to ask two main questions: 1) which did you like most, and why, and 2) what would you improve about the puzzles? This is still the early stage of development, so we're trying to pin down the best puzzle permutations possible. Thanks!

[jgrams]

I didn't find these fun and interesting to solve: they just seem tedious. But maybe I'm missing something: are there deductions to make to find the solutions, or are you just guessing your way through the space? Obviously at each end of the equation there are limited possibilities (you often can't use subtraction or division), but beyond that?  And are there connections between the set of puzzles in a ring?  The "ring of puzzles" sounds like a cute idea but in practice it felt like a set of six completely unconnected number puzzles and I ended up just looking at the table at the bottom of the page.

Aside from that, your software is obviously buggy and I don't trust it.  The PDF says "Each puzzle in the book is designed to have a single correct solution."  But the very first line of your first worked example has at least two solutions: you give 1+12+3-6-5-4=1, but 1*12/3+6-5-4=1 works as well.  The color puzzles say that "operators of the same type are found in boxes of the same colour," but then both the worked example and both of the puzzles have single boxes of at least one colour, which...don't do anything??? And one of them has only three colours of boxes, so it looks like you tried and failed to write code to remove unnecessary boxes? Unless you meant to require that no coloured box can contain the same operator as a different coloured box, in which case you need to put that in the instructions. And the pseudo-zen phrasing of that instruction (like the naming of the puzzles) seems horribly cheesy and fake. Just say "boxes of the same colour must contain the same operator" and be done with it.

Also with the colour puzzles there isn't any ambiguity that I saw.  For instance, in the puzzle on page 15, I checked all the possible combinations for each of the final three lines (with the blue boxes).  Each line has only one solution!  If there were ambiguity then it would add something to the puzzle: you'd have to match up the operators in the coloured boxes to solve it (though I'm not sure these puzzles need a bigger combinatorial explosion).  If it's meant to make the puzzles easier by filling in some of the operations or eliminating certain possibilities for you, then you would need to actually say that in the instructions instead of trying to be all mysterious. And that would make them easier than the basic ones, and you probably shouldn't imply that they're more complex (as you did in your message).

At that point I was thoroughly fed up so I didn't try the other two puzzle layouts. Probably I should have given up earlier and then this message would be slightly less of a rant.