# Blog

## Archive

Show me a random blog post**2019**

### Jun 2019

Proving a conjecture### Apr 2019

Harriss and other spirals### Mar 2019

realhats### Jan 2019

Christmas (2018) is over**2018**

**2017**

**2016**

**2015**

**2014**

**2013**

**2012**

## Tags

go programming the aperiodical misleading statistics books harriss spiral python realhats noughts and crosses sound pac-man speed nine men's morris flexagons electromagnetic field manchester dragon curves chebyshev trigonometry sorting geometry javascript christmas hats football light accuracy oeis people maths hexapawn statistics reuleaux polygons rugby triangles bodmas christmas card arithmetic london underground pythagoras game show probability games braiding frobel data golden ratio gerry anderson binary sport puzzles approximation inline code folding tube maps mathslogicbot map projections weather station machine learning tennis radio 4 menace palindromes reddit royal baby london national lottery world cup asteroids polynomials stickers video games dates curvature coins plastic ratio twitter dataset folding paper wool mathsteroids countdown chalkdust magazine bubble bobble fractals manchester science festival error bars raspberry pi final fantasy rhombicuboctahedron propositional calculus martin gardner interpolation chess platonic solids captain scarlet game of life craft aperiodical big internet math-off a gamut of games european cup graph theory logic golden spiral mathsjam matt parker probability php news pizza cutting draughts latex ternary estimation cross stitch**2018-04-29**

Two years ago, I built a copy of MENACE (Machine Educable Noughts And Crosses Engine). Since then, it's been to many Royal Institution masterclasses, visted Manchester and met David Attenborough. When I'm not showing them off, the 304 matchboxes that make up my copy of MENACE live in this box:

This box isn't very big, which might lead you to wonder how big MENACE-style machines would be for other games.

### Hexapawn (HER)

In

*A matchbox game learning-machine*by Martin Gardner [1], the game of Hexapawn was introduced. Hexapawn is played on a 3×3 grid, and starts with three pawns facing three pawns.The pieces move like pawns: they may be either moved one square forwards into an empty square, or take another pawn diagonally (the pawns are not allowed to move forwards two spaces on their first move, as they can in chess).
You win if one of your pawns reaches the other end of the board. You lose if none of your pieces can move.

The game was invented by Martin Gardner as a good game for his readers to build a MENACE-like machine to play against, as there are only 19 positions that can face player two, so only 19 matchboxes are needed to make HER (Hexapawn Educable Robot). (HER plays as player two, as if player two plays well they can always win.)

### Nine Men's Morris (MEME)

In Nine Men's Morris, two players first take turns to place pieces on the board, before taking turns to move pieces to adjacent spaces. If three pieces are placed in a row, a player may remove one of the opponent's pieces. It's a bit like Noughts and Crosses, but with a bit more chance of it not ending in a draw.

In

*Solving Nine Men's Morris*by Ralph Gasser [2], the number of possible game states in Nine Men's Morris is given as approximately \(10^{10}\). To build MEME (Machine Educable Morris Engine), you would need this many matchboxes. These boxes would form a sphere with radius 41m: that's approximately the length of two tennis courts.As a nice bonus, if you build MEME, you'll also smash the world record for the largest matchbox collection.

### Connect 4 (COFFIN)

In

*Symbolic classification of general two-player games*by Stefan Edelkamp and Peter Kissmann [3], the number of possible game states in Connect 4 is given as 4,531,985,219,092. The boxes used to make COFFIN (COnnect Four Fighting INstrument) would make a sphere with radius 302m: approximately the height of the Eiffel Tower.In

*Solving the game of Checkers*by Jonathan Schaeffer and Robert Lake [4], the number of possible game states in Draughts is given as approximately \(5\times10^{20}\). The boxes needed to build DOCILE (Draughts Or Checkers Intelligent Learning Engine) would make a sphere with radius 151km.If the centre of DOCILE was in London, some of the boxes would be in Sheffield.

### Chess (CLAWS)

The number of possible board positions in chess is estimated to be around \(10^{43}\). The matchboxes needed to make up CLAWS (Chess Learning And Winning System) would fill a sphere with radius \(4\times10^{12}\)m.

If the Sun was at the centre of CLAWS, you might have to travel past Uranus on your search for the right box.

### Go (MEGA)

The number of possible positions in Go is estimated to be somewhere near \(10^{170}\). To build MEGA (Machine Educable Go Appliance), you're going to need enough matchboxes to make a sphere with radius \(8\times10^{54}\)m.

The observable universe takes up a tiny space at the centre of this sphere. In fact you could fit around \(10^{27}\) copies of the universe side by side along the radius of this sphere.

It's going to take you a long time to look through all those matchboxes to find the right one...

#### References

[3]

**by***Symbolic classification of general two-player games***Stefan Edelkamp and Peter Kissmann**. in Advances in Artificial Intelligence (edited by A.R. Dengel, K. Berns, T.M. Breuel, F. Bomarius, T.R. Roth-Berghofer), 2008. [link][4]

**by***Solving the game of Checkers***Jonathan Schaeffer and Robert Lake**. Games of No Chance 29, 1996. [link]### Similar posts

MENACE | MENACE in fiction | MENACE at Manchester Science Festival | The Mathematical Games of Martin Gardner |

### Comments

Comments in green were written by me. Comments in blue were not written by me.

**Add a Comment**

2018-11-16g0mrb