Hello everyone! My name's Mark Johnson, and 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 looplike 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 longterm 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/ ... pdmdl=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!
New "paper puzzle" game  feedback requested!
Re: New "paper puzzle" game  feedback requested!
Hi Mark, thanks for sharing this. It's always good to hear new puzzle ideas.
Here are (from a purely puzzle solving perspective) some brief thoughts:
First off, I like the name!
Making the rules as clear as possible is usually desirable in the puzzle solving world. I think I'd try and draw attention to the fact that the arithmetic is being evaluated one operation at a time. People are very attached to BODMAS and might get confused/annoyed if it isn't clear that isn't what they are supposed to be doing. Although admittedly I'm sure there's a mental arithmetic puzzle in the Times where you perform specified calculations along a ladder which is the same format as this.
I suppose it's kind of implicit, but are the results of all operations specifically (positive? nonzero?) integers and not fractions? This obviously affects how you might treat the / and  operations.
Uninatsu:
I think with all the numbers given (and the operations missing) the presentation with the 6 strips is much more convenient than the ring configuration. In fact you aren't really using the ring configuration at all from a solving point of view. You could just as well have 6 different equations presented, without the ring, and have pretty much the same solving experience.
I think to bring the ring mechanics into play, you might start giving some (maybe not all) of the operations as fixed links for all of the equations, and instead have some of the numbers missing, to be filled in.
Chromanatsu:
I think the same thing applies. Combining with the above, I note that having diagonal sequences which shift the colour one along as you move down the strips does pretty much the same thing.
Maxinatsu:
I like the idea here. Perhaps for solving convenience you might have some dedicated space to write in intermediate totals? This one I,d definitely stick with the ring presentation though  with spaces in which to fill in the operations. I'd also experiment with perhaps having some of the numbers missing as well  maybe you'd need to add in a couple of operations to help things along.
Hexanatsu:
A couple of thoughts I had here. Firstly, you could turn this into a kind of maze, by having exactly one such loop through the Hex grid which works out. Secondly, it'd be nice if the middle hexagon also had the property. I imagine this type is pretty constrained, so as with the above, I'd be tempted by leaving some of the numbers to be filled in as well.
Here are (from a purely puzzle solving perspective) some brief thoughts:
First off, I like the name!
Making the rules as clear as possible is usually desirable in the puzzle solving world. I think I'd try and draw attention to the fact that the arithmetic is being evaluated one operation at a time. People are very attached to BODMAS and might get confused/annoyed if it isn't clear that isn't what they are supposed to be doing. Although admittedly I'm sure there's a mental arithmetic puzzle in the Times where you perform specified calculations along a ladder which is the same format as this.
I suppose it's kind of implicit, but are the results of all operations specifically (positive? nonzero?) integers and not fractions? This obviously affects how you might treat the / and  operations.
Uninatsu:
I think with all the numbers given (and the operations missing) the presentation with the 6 strips is much more convenient than the ring configuration. In fact you aren't really using the ring configuration at all from a solving point of view. You could just as well have 6 different equations presented, without the ring, and have pretty much the same solving experience.
I think to bring the ring mechanics into play, you might start giving some (maybe not all) of the operations as fixed links for all of the equations, and instead have some of the numbers missing, to be filled in.
Chromanatsu:
I think the same thing applies. Combining with the above, I note that having diagonal sequences which shift the colour one along as you move down the strips does pretty much the same thing.
Maxinatsu:
I like the idea here. Perhaps for solving convenience you might have some dedicated space to write in intermediate totals? This one I,d definitely stick with the ring presentation though  with spaces in which to fill in the operations. I'd also experiment with perhaps having some of the numbers missing as well  maybe you'd need to add in a couple of operations to help things along.
Hexanatsu:
A couple of thoughts I had here. Firstly, you could turn this into a kind of maze, by having exactly one such loop through the Hex grid which works out. Secondly, it'd be nice if the middle hexagon also had the property. I imagine this type is pretty constrained, so as with the above, I'd be tempted by leaving some of the numbers to be filled in as well.

 Posts: 390
 Joined: Mon 21 Jun, 2010 2:02 pm
Re: New "paper puzzle" game  feedback requested!
Don't usually respond to requests like this, but Tom has encouraged me to say something. The Hexanatsu format looks by far the most interesting. How constrained is the set of solutions for a single hexagon? Could we combine hexagons with other polygons to expand the solution space? Why not allow anticlockwise travel? I agree that leaving out some of the numbers would make a more satisfying solve. And the maze idea is a great one. You could have intermediate checkpoints with target totals.