How do I simulate 8-faced dice with only 6-faced dice?
I have been given the hint that $6^3$ is divisible by 8.
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3Hint: Can you simulate 8-faced dice with coins? And can you simulate coins with 6-faced dice? – celtschk Oct 01 '16 at 05:23
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is that correct to use binary number? – Y.X. Oct 01 '16 at 05:27
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If you mean what I think you mean, then yes. – celtschk Oct 01 '16 at 05:29
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Using the hint: Think about the number of ways you can roll three $6$-sided dice, and how you might be able to partition them into $8$ different groups of possibilities, each with the same size.
Carl Schildkraut
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But how can I think of it exactly? I have tried to think about it but can hardly get the answer. – Y.X. Oct 01 '16 at 04:50
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Well, Y.X., start at the beginning. How many ways can you roll three 6-sided dice? – Gerry Myerson Oct 01 '16 at 05:00
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@GerryMyerson I just do not know how to define the number correspond to each result. Could you please give me a solution please? I have tried but fail to get the solution. – Y.X. Oct 01 '16 at 05:24
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1@Y.X. Here's another hint. How can you make one roll of a 6-sided die like the flip of a coin? – Carl Schildkraut Oct 01 '16 at 05:37
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OK, 216. Now, if you partition those 216 into 8 different groups of the same size, Y.X., how big will each group be? – Gerry Myerson Oct 01 '16 at 10:21
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Roll the die three times subtracting 1 from each result. Arrange the outcomes as the digits of the base-6 figure $d_0d_1d_2$. Converting this number to decimal you'll have a number between 0 and 215. Assign 1 as the outcome of your 8-faced die when the number is between 0 and 26, 2 when the number is between 27 and 53 and so on.
N74
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throw the dice, multiply the results together, divide by 27, round the result up to a whole number
