Roll a standard pair of six-sided dice, and note the sum. There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12. Find all other pairs of six-sided dice such that:

1. The set of dots on each die is not the standard {1,2,3,4,5,6}.
2. Each face has at least one dot.
3. The number of ways of obtaining each sum is the same as for the standard dice. Roll a standard pair of six-sided dice, and note the sum. There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12. Find all other pairs of six-sided dice such that:

1. The set of dots on each die is not the standard {1,2,3,4,5,6}.
2. Each face has at least one dot.
3. The number of ways of obtaining each sum is the same as for the standard dice. @Mathematics

Question

Roll a standard pair of six-sided dice, and note the sum.  There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12.  Find all other pairs of six-sided dice such that:

1. The set of dots on each die is not the standard {1,2,3,4,5,6}.
   2. Each face has at least one dot.
   3. The number of ways of obtaining each sum is the same as for the standard dice. Roll a standard pair of six-sided dice, and note the sum.  There is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12.  Find all other pairs of six-sided dice such that:

1. The set of dots on each die is not the standard {1,2,3,4,5,6}.
   2. Each face has at least one dot.
   3. The number of ways of obtaining each sum is the same as for the standard dice. @Mathematics

anonymous · Answer

hmm... I can't seem to google the answer to this :-(

time to solve it either analytically or using Python :-D

anonymous · Answer

Can we have dies with blank faces?

anonymous · Answer

oh i'm silly I didn't read all of it :-P

anonymous · Answer

hint: Represent each die using a generating function.

anonymous · Answer

yeah generator objects in python

anonymous · Answer

lol do u want the  answer?

anonymous · Answer

wait I want to solve it using Python

anonymous · Answer

okay lol

anonymous · Answer

before the killjoy expert math guys come over and ruin my fun with some fancy theorem :-(

anonymous · Answer

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

anonymous · Answer

lol u are a funny guy. :p

anonymous · Answer

heres the answer
The only alternative dice that meet the conditions are {1,2,2,3,3,4} and {1,3,4,5,6,8}.

anonymous · Answer

exactly: http://mathworld.wolfram.com/SichermanDice.html

anonymous · Answer

hurray for Google.

anonymous · Answer

lol