About eighteen months ago I was given a set of Grime Dice and it has taken me that long to have the idea to make a knitted set.

Grime Dice are a set of five dice with the numbers arranged so that you can always choose a dice that will, over time, beat the dice chosen by your opponent. They are known as non-transitive dice. Using dice A, B and C, A will beat B, B will beat C and, amazingly, C will beat A. Several sets of non-transitive dice have been documented. Grime Dice are slightly different because you can use a set of 3 or a set of 5 and you can change the order in which they work by choosing to use two sets of dice. There are several different tricks that can be employed to beat the opposition. If the opponent works out the trick you are using you can use different rules to ensure that you will still win. You can even play against two opponents at the same time - and beat both of them.

The chances of winning rely on the probability of the score of each dice. The names of the colours are very important to learning the tricks to enable you to win.

Grime Dice were discovered by a young mathematician named Dr James Grime. James is The Enigma Project Officer at the University of Cambridge. He is also well-known to many people as one of the presenters of Numberphile videos and an organiser of MathsJam. He occasionally pops up on TV and radio talking on various aspects of Maths. In his spare time he likes juggling, unicycling and other circus skills.

It seemed fitting to combine the love of juggling with the maths of the dice to create Grime Dice Juggling Balls.

James made a video of him juggling the dice and briefly explaining the sequences.

The main instructions are for knitted juggling balls. They can be made in any yarn. Those in the photo used DK in red, blue, olive, yellow and magenta. The colours are very important and should not be changed. Some of the links below have older versions of Grime Dice that are not coloured in the way that was developed later.

You can also make dice in plastic canvas, or use the nets to make paper dice.

The pattern does not include information about the reason for the choice of colours or about how to use the dice to ensure that you will win. This information has been covered, at length, by James, and other people, in various videos and teaching resources.

http://www.mathsgear.co.uk/non-transitive-dice-set-of-5/
http://en.wikipedia.org/wiki/Nontransitive_dice
http://grime.s3-website-eu-west-1.amazonaws.com/
http://www.think-maths.co.uk/downloads/grime-dice-lesson-resources
http://www.teachmaths-inthinking.co.uk/activities/grime-dice.htm