History
What was Rithmomachia?
Machia is Battle by Numbers: a daily puzzle that revives Rithmomachia, the game European scholars played for five centuries alongside chess. One board a day, the same board for everyone. Capture pieces with arithmetic: equal numbers, sums, and multiplication across the gap. Free, in your browser, no account, no ads, ever. By Centone Games.
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What kind of game was it?
A board game of numbers. Every piece carried a value, and most captures were made by arithmetic: equal numbers, sums, and in some versions multiplication across the gap.
The earliest account of it was written at Würzburg around 1030 by a churchman named Asilo. Hermannus Contractus, a monk of Reichenau, refined its rules soon after. It was built on the Arithmetic of Boethius, the standard textbook of the schools. Two armies, the evens and the odds, met on a board usually eight squares by sixteen. The pieces were rounds, triangles and squares, each carrying a number, with a stacked pyramid on each side. A piece was taken if an enemy piece of the same number could move onto it. It was also taken if two enemy pieces that could both reach it had numbers adding up to its own, and some rulebooks allowed products, differences and quotients too. In some versions a smaller piece took a larger one at a distance, if its number multiplied by the number of empty squares between them gave the larger. A piece hemmed in so that it could not move was lost as well. The highest victories came from setting three or four pieces in the enemy's camp, their numbers forming a progression.
Who played it?
European scholars, for five centuries, alongside chess.
It began in the monastery and cathedral schools as an aid to arithmetic, one of the four mathematical arts beside geometry, music and astronomy. Later it was played at the universities. In the thirteenth century Roger Bacon counted it as part of practical arithmetic and called it a game of wisdom. Thomas More gave the islanders of Utopia (1516) a game he calls a battle of numbers, in which one number captures another. It was printed too: in Latin from 1482, in French in 1554, in English in 1563 under the name the Philosophers' Game, and in Italian in 1572.
Why did it disappear?
Because the mathematics it taught went out of date. The game was a lesson in Boethius's number theory, and it was played only as long as that theory was taught. Shortly after 1600, as the teaching of mathematics changed, its popularity fell for good. It never had one set of rules either: they varied from one manual to the next. Chess took its place among the learned. In the seventeenth century its rules were printed as an appendix to a German book on chess, and after that it lived on as a curiosity in German chess books. No board or piece from the Middle Ages is known to survive. The game is known from manuscripts and printed books.
What does Machia keep, and what does it change?
Machia keeps the idea: pieces are numbers, you capture by arithmetic, with equality, sum and eruption, and each side has a leader to take, as the old game's pyramid was its king. It changes the scale: one board a day, the same board for everyone, a machine that answers every move you make, and the forge, where two of your pieces become one. Free, in your browser, no account.
Why does Machia look like a tapestry?
The Bayeux Tapestry is the visual inspiration: the board is drawn as woven cloth, with a stitched frame and a title band. See how to play
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