Mathematical recreation

January 6, 2013
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(This article was originally published at Learn and Teach Statistics and Operations Research, and syndicated at StatsBlogs.)

Here in New Zealand it is still the summer holidays, and it is difficult to feel too excited about topics of great moment, even if it is the International Year of Statistics and the start of Mathematics of Planet Earth 2013!

While the sun shines in a clear blue Christchurch sky, in the interests of mathematical recreation I will tell you about Rogo, a new number puzzle that we hope will soon become as popular as Sudoku.

A Rogo puzzle

A  simple Rogo puzzle

We came up with the idea for Rogo a few years ago. I have always loved board games, and was trying to invent one based around the sport of Rogaining. (I still have hopes to bring that one to fruition one day.) Instead we came up with a puzzle that can be done with pen and paper, or on an iPhone/iPad/iPod touch. It is based on the traveling salesperson problem, with prize collection and subset selection, all on a rectilinear grid.

It’s surprisingly fun and engrossing (and to use a somewhat overused term, addictive!).

Children as young as six or seven like to play on the Rogo app, as do adults all over the world. Our greatest fan is Martin, in Austria, and having solved the 384 puzzles on the iPad, he is keen for us to make another set. I think we need to sell some more of our current version first!

You can see a YouTube video on how to play on the iPhone here:

Or an early Youtube video on how to solve Rogo on paper here:

You can buy the app here (sorry only iOS at present): Link to the AppStore. (Please do!)

You can get daily paper puzzles here: Daily puzzles

We have a website dedicated to Rogo, where there is a useful page about how Rogo can be used in teaching. This is aimed at school level problem-solving, science fair, extension and numeracy development. For a University course involving heuristics, Rogo is a great medium through which to illustrate and teach different search algorithms.

We have done some research into what makes a Rogo difficult. We came up with twelve potential  factors in the determination of difficulty.  You can read about that in our paper:Determining Degree Of Difficulty In Rogo, A TSP-based Paper Puzzle

Solving Rogo

The computational solution of Rogo is mathematically challenging. In the early days of developing our algorithm my laptop would overheat and shut down if I tried to solve too many bigger Rogos.

Hakan Kjellerstrand wrote about solving Rogo in a blog about constraint programming.

Recently Chris Kuip blogged about Rogo in AIMMS Rogo Solver using constraint programming

You can read about our algorithm in the Journal of Information Processing.

Have fun!




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