Not so simple games

Just sit right back and you’ll hear a tale,
A tale of a fateful trip
That started from a Rubik’s Cube
(Erno gets a hat tip).

The authors were the mighty Igor Kriz,
Paul Siegel brave and sure
With simple groups they tried that day
for a three game tour, a three game tour.

The puzzles started getting tough,
The Monster game was tossed,
If not for the courage of the fearless pair
The new games would be lost, the new games would be lost.

The pair made games from the math of three
Sporadic simple groups
With M12
M24 too,
(From Émile Mathieu, not his wife)
The final star*
From Professor John Co-on-way
Here on Sciam Isle!

* Dotto, based on Conway’s group .0

See this article in Scientific American about how the authors, inspired by the Rubik’s cube, used sporadic simple groups to create new games. The games can be found here.

Suddenly Tic-Tac-Toe isn’t boring!

They were laughing and playing Tic-Tac-Toe. At 7:45am, no less. So I wandered into the math center to see just what was so exciting to the handful of math majors gathered around the computer before their Algebra class.

It turns out they were playing Tic Tac Toe on a Klein Bottle. Several of our students went to the Hudson River Undergraduate Mathematics Conference this past weekend, and the keynote speaker, Jeff Weeks (a freelance mathematician) had presented several geometry games. The students were playing Torus Games, in which traditional games like tic tac toe or billiards are played on a torus or on a Klein bottle. And I was jealous, because suddenly Tic Tac Toe looked like fun, so I downloaded the software myself and played a game. Here’s a screenshot of me having beat the computer on the Klein Bottle:

Screenshot posted with permission

Because it’s a Klein bottle, when you move down to the bottom it’s the same as moving up, but with left and right switched; the sides are likewise connected, although you stay in the same row. You can even hold down the cursor and move the board around to see how it behaves like an infinite board. It reminded me a little bit of Möbius Chess.

There’s a bunch of other free stuff, too, at Jeff’s main site of Topology and Geometry Software, like Kali for making wallpaper pattern designs and the 3d Kaleido Tile. (I had a lot of fun moving the center point and seeing solids morph into other solids.)

Meanwhile, the students had moved on to exploring the shape of the universe. Not too bad for a Monday morning.

Sudoku and Kakuro

In recent years many people have played Sudoku, a number game in which a nine-by-nine grid is filled with the digits 1-9 so that each row, each column, and each group of nine squares contains exactly one of each digit.