mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 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.
MEME: Machine Educable Morris Engine
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.
COFFIN: COnnect Four Fighting INstrument

Draughts/Checkers (DOCILE)

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.
DOCILE: Draughts Or Checkers Intelligent Learning Engine
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.
CLAWS: Chess Learning And Winning System
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.
MEGA: Machine Educable Go Appliance
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...

A matchbox game learning-machine by Martin Gardner. Scientific American, March 1962. [link]
Solving Nine Men's Morris by Ralph Gasser. Games of No Chance 29, 1996. [link]
Symbolic classification of general two-player games by 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]
Solving the game of Checkers by Jonathan Schaeffer and Robert Lake. Games of No Chance 29, 1996. [link]
                        
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
Kind of like the "Blue Brain Project". They got a worm and fruitfly brain on the computer, I wanted to download the fruitfly brain for 2GB USB stick but it was over 12 TB. They uploaded half a mouse brain on their project so far.
Willem
                 Reply
Would Love to play with Coffin/Coffin2. Do you have the code on git or a JS/web version?... been kind of thinking of coding a version that only makes the match boxes as it needs them (to save on memory) but I heard you already have a version with optimizations (and my coding skill is rough at best)
John
                 Reply
Are you aware of any actual implementations of anything in matchboxes, games or otherwise?
Jam
                 Reply
Of course, to make CLAWS, you will have to leave a large gap in the centre of the matchbox sphere, to avoid the very real danger of fire. Furthermore, some redundancy is needed, to replace the boxes which will be damaged by the myriad hard objects which are whizzing around the solar system. For this latter reason alone, I propose that the machine would be impractical to make! ;-D
g0mrb
      ×1           Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "hexagon" in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

errors national lottery signorini conditions pythagoras mathslogicbot gaussian elimination stirling numbers fonts geometry inline code rugby dates countdown stickers pi palindromes polynomials fence posts edinburgh estimation cross stitch draughts talking maths in public accuracy interpolation databet go radio 4 chalkdust magazine hannah fry simultaneous equations manchester london underground noughts and crosses graphs big internet math-off correlation christmas pac-man php propositional calculus curvature sound london map projections programming recursion dragon curves sorting boundary element methods triangles menace ucl raspberry pi exponential growth 24 hour maths people maths dataset european cup weak imposition pascal's triangle finite element method quadrilaterals mean matrix multiplication data visualisation reuleaux polygons harriss spiral inverse matrices fractals anscombe's quartet wave scattering folding tube maps oeis mathsjam data hexapawn frobel advent calendar world cup sport live stream hats golden ratio pizza cutting computational complexity flexagons turtles machine learning manchester science festival nine men's morris phd plastic ratio newcastle graph theory ternary finite group probability binary guest posts matt parker matrices pi approximation day dinosaurs geogebra chebyshev tennis speed zines arithmetic logo reddit chess crossnumber numbers determinants mathsteroids golden spiral game show probability python video games crochet platonic solids puzzles news preconditioning a gamut of games latex squares games convergence braiding books tmip matrix of cofactors misleading statistics football martin gardner approximation matrix of minors trigonometry royal institution royal baby weather station final fantasy gather town javascript standard deviation craft realhats runge's phenomenon the aperiodical asteroids bubble bobble logs statistics wool folding paper gerry anderson captain scarlet cambridge hyperbolic surfaces datasaurus dozen logic game of life light christmas card numerical analysis electromagnetic field bempp coins bodmas error bars sobolev spaces rhombicuboctahedron youtube

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024