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]
×1      ×1            ×2      
(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   ×1   ×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 "s" then "e" then "g" then "m" then "e" then "n" then "t" in the box below (case sensitive):

Archive

Show me a random blog post
 2025 

Jan 2025

Christmas (2024) is over
Friendly squares
 2024 
▼ show ▼
 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

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2025