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Ludyssey - Mathematical journey through ancient games

Workshop - exhibition

video Ludyssey

download the overview pdf:  Ludyssey- English

“Consider the seed of your generation:
you were not made to live like brutes,
but to play games and make them science! ”

Isn’t that what Dante’s Ulysses used to say in order to spur his fellow travelers (and players)?
In his wandering back and forth the Mediterranean horizons, Ludysseus was trying to trace the deep roots of the peoples through their games and the mathematics hidden therein. He analysed the game strategies, seeking and studying mathematically the game errors.
Ludyssey is a journey that takes you from the geometry of the Archimedean Ostomachion (square split into 14 different shapes) to the probability hidden in the variants of Backgammon (Ludus Duodecim Scriptorum for the Romans, Tavli for Greeks and Turks). From the periodic configurations of Mancaley (Syrian game of sowing) to the binomial law of Moroccan Sig, and finally to the arithmetic taught in medieval Italy and France through Rithmomachia, the “Battle of Numbers” (a kind of chess with sums and products).

“And turning our stern toward morning,
we made wings of oars for our mad flight,
still playing chess and hide-and-seek”

By Cesco Reale (Festival of Mathematical Games). In collaboration with MateFitness (CNR-PSC) and with CEMEA Veneto.
Under the patronage of the Swiss Museum of Games and with the financial support of Festival della Scienza.

The animators illustrate the different games of Ludyssey and let people play, explaining the historical-cultural context where they are (or were) played and the general rules. Afterwards the public is invited to analyse some game situations that have links to mathematics: they will be asked to find the error in some movements or game configurations, and then to study the mathematical part that allows to correct the error. The activity is thought for schools and festivals, but also for a more demanding public, as it can be adapted to different levels. Moreover Ludyssey is also an exhibition, with panels to read and games to admire.

Past events:

– Festival dellaScienza 2010, Genova

InfinitaMente 2011,  UnivVerona

 SettimanadellaMatematica 2012, Univ. Brescia


– Ostomachion. Pick’s theorem, which is the area of the following figures? Try to reproduce them with the game pieces. In how many ways can you rebuild the square? Computer animations of the possible square reconstructions and their graph.

– Mancala. The remainder of the division. Which moves allow me to threaten a capture? Walking groups and periodic configurations. Ethno-mathematics: comparison between the analyses of mathematicians and local experts.

– Sig: binary dice and binomial law. Video of Saharawi women playing in the desert.

– Rithmomachia: presentation of Boethius’ Arithmetica. Arithmetics, geometry and music in Pythagorean philosophy. Arithmetic, geometric and harmonic sequences.

– Backgammon: comparison with the Ludus Duodecim scriptorum (ancient Roman game) and the modern versions in Greece; in this situation what is the best move to minimize the probability that the piece will be captured?

MATERIALS. The exhibition consists of 10 panels (A1-size 84 x 60) and 20 wooden games used by the public during the workshops. Necessary space: 50-100 m2.



– Marc Chemillier (Univ. Caen). Eléments pour une ethnomathématique de l’awélé (Mathematics and Social Sciences n. 181, 2008)
– Alex de Voogt (Univ. Leiden). The archaeology and anthropology of Syrian mancala (Board Game Studies 2010)
– Marino Carpignano (Progetto Abstrakta).
– Univ. Lisboa. Matemática em Jogo — exposição virtual.


– Federico Peiretti (Progetto Polymath). Stomachion, il puzzle di Archimede.
– Stomachion (Visualization of the 268 basic solutions)
Fan Chung and Ron Graham (Univ. California San Diego). A tour of Archimedes’ Stomachion (detailed combinatorical analysis of the Stomachion).
– The Walters Art Museum. The story of the Archimedes’ Palimpsest to 2000 – DVD.
– Kelli Nipper – Picky Nicky and Pick’s Theorem (how to derive the Pick’s formula)’sTheorem.html
– Heather Bridges – Pick’s and Euler’s Theorems.


– Laurent Bussard. Règles du jeu de Sig de Mauritanie.
– Tim Hull. Globaltimoto: A Quest for Gameplay. (Rules, photos, videos).
– Thierry Depaulis, Jeux de parcours du monde arabo-musulman (Board Game Studies 2001)
– Site culturel du Sahara (vidéos).


– Peter Mebben. Die Arithmomachia des Abraham Ries und weitere neuzeitliche Überlieferungen der Rithmomachie (Board Game Studies 1999)
– José M. Núñez Espallargas (Univ. Barcelona). La aritmética de Boecio y la ritmomaquia: teoría y práctica del juego medieval de los sabios. (Anuario de Estudios Medievales, 2004).
– Alessandro Fedi (Assoc. Terra di Prato). Rithmomachia ovvero il Ludus Philosophorum (2007).
– Boethius. De Institutione arithmetica (505).
– Blog about Rithmomachia (Paesi Bassi, 2004)
– J. F. Gilles. Rythmomachie, diverses règles du jeu.


– Dario De Toffoli, Il grande libro del Backgammon, Stampa Alternativa, 2008, ISBN 978-88-6222-035-4