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Number Theory/Dice - Cube Shape Design.

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Question
Dice
Dice  
Dear Prof Vijilant

http://en.wikipedia.org/wiki/Dice

We use Dice in various indoor games viz Snakes and Ladders, Ludo, Business etc. Dice is cube shape, just curious to know regarding the design i.e. Six sides numbered with each side with 1,2,3,4,5,6.

What could be the reason for designing a Dice with a Cube shape ?
Six is an even number. Can we also have dice manufactured as a Pentagonal shape (i.e. 5 sides numbered with 1,2,3,4,5) or Heptagon (i.e. 7 sides numbered with 1,2,3,4,5,6,7.
i.e. Odd Number Dice.

Some Games are also played with more than One Dice i.e Two Dice.

Can Games be played with One Dice a Cube shape and another Dice with a Heptagon Shape ?

Is it something to do with Probability Theory ?. If we change the Dice design, will there be also probable changes in game business rules viz Snakes and Ladders, Ludo etc ?.

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Answer
Hello Prashant

I'm very busy marking exams at the moment so haven't the time to study the wiki article.  I'll just give a few thoughts.

First of all, for most games we need a uniform distribution.  That is, equal probabilities for the outcomes giving what we call a fair die.  The cube is a regular solid, so this is fine, as are the tetrahedron(4), the octahedron(8), the dodecahedron(12) and the icosahedron(20).
For other numbers, we can use spinners, a regular polygon made of resistant material with a spike through its centre and spun by twisting with the fingers.  Also, a roller in the shape of a prism with two regular polygonal faces and rectangular faces.  Two of these were used in the cricket game 'OWZAT' which I used to play.

A spinner or roller could be devised to simulate a game in which the scores of two ordinary dice were added. A roller would need 36-gon faces.  A spinner would have sectors whose angles were in the same proportion as the probabilities.  For example double six, or 12 would have an angle of 10 degrees.

Best wishes

vijilant

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Vijilant

Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.

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