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# Modifying two standard dice

### #1

Posted 28 March 2013 - 06:25 PM

Assume you have a standard dice with labels 1, 2, 3, 4, 5, 6 on each respectively. Pretend you are playing a simple game where you roll the two dice and add their values together. Is it possible to relabel the dice using positive integers in such a way that if you play the same dice game you would have an equal probability of rolling the same sums?

Note: What I mean by relabeling is not simply rotating all of the numbers on the dice where by each dice still contains the same six numbers but rather actually making new dice that has a different set of six integers than the original. (e.g. one dice could be 1, 2, 3, 4, 5, 9 and the other could be 1,1,1,1,1,1 ... would this pair produce the same sum probabilities as the original?--in short, no )

### #2

Posted 28 March 2013 - 10:30 PM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 28 March 2013 - 10:46 PM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #4

Posted 28 March 2013 - 10:49 PM

**Edited by BMAD, 28 March 2013 - 10:50 PM.**

### #5

Posted 29 March 2013 - 09:30 AM

Let me rephrase the op. the probability of rolling a 2 with two normal dice is 1/36. The probability of rolling a 3 is 2/36. Can you relabel the dice so that you still get these probabilities and all others using different dice configurations

### #6

Posted 29 March 2013 - 04:58 PM

Assume you have a standard dice with labels 1, 2, 3, 4, 5, 6 on each respectively. Pretend you are playing a simple game where you roll the two dice and add their values together. Is it possible to relabel the dice using positive integers in such a way that if you play the same dice game you would have an equal probability of rolling the same sums?

Note: What I mean by relabeling is not simply rotating all of the numbers on the dice where by each dice still contains the same six numbers but rather actually making new dice that has a different set of six integers than the original. (e.g. one dice could be 1, 2, 3, 4, 5, 9 and the other could be 1,1,1,1,1,1 ... would this pair produce the same sum probabilities as the original?--in short, no )

Here's an answer

### #7

Posted 29 March 2013 - 05:05 PM

Here's an answerAssume you have a standard dice with labels 1, 2, 3, 4, 5, 6 on each respectively. Pretend you are playing a simple game where you roll the two dice and add their values together. Is it possible to relabel the dice using positive integers in such a way that if you play the same dice game you would have an equal probability of rolling the same sums? Note: What I mean by relabeling is not simply rotating all of the numbers on the dice where by each dice still contains the same six numbers but rather actually making new dice that has a different set of six integers than the original. (e.g. one dice could be 1, 2, 3, 4, 5, 9 and the other could be 1,1,1,1,1,1 ... would this pair produce the same sum probabilities as the original?--in short, no )

Spoiler for

Nice.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #8

Posted 29 March 2013 - 06:15 PM

### #9

Posted 29 March 2013 - 06:42 PM

Spoiler for positive integers

Maybe OP meant non-negative?

I think I have a proof there is no other solution. Construct the table.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #10

Posted 29 March 2013 - 06:57 PM

Spoiler for positive integers

Maybe OP meant non-negative?

I think I have a proof there is no other solution. Construct the table.

Missed the point about positive integers. I agree with bonanova, in that case

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