[bonanova]

Alex and his friends Ian and Davey were enjoying

some cold ones at Morty's last night when Alex pulled

a small pouch out of his pocket and began to tell his

story.

So this fellow I met claimed he mastered the art of

loading dice, and he was able to separately adjust the

chances of each of the faces showing. We got to talking,

and I asked him to make a pair of dice that would make

all the possible results, 2, 3, 4, ... 10, 11 and 12,

appear with equal chances. Here they are. And

he held them up for all to see.

No way, said Davey, who was no mathematician, to

be sure, but this seemed beyond possibility.

So you're an unbeliever, replied Alex. Then watch this;

and Alex rolled the dice 5 times, getting 2, 5 12, 9 and 6.

How many times would you have to roll an honest pair

of dice to see snake eyes and box cars in 5 rolls?

Jamie heard the commotion and strolled over to the table.

Here, let me try. And Jamie rolled 3, 10, 8, 2 and 11.

Well, these are no normal dice, that's for sure, he said.

What are you going to do with them?

Haven't decided yet, Alex replied. For now, maybe just

a few little wagers with some of my, ahem, acquaintances.

Ian had been thinking for a bit. They're special dice,

to be sure, he said. But I'm quite certain they're not

what you say they are.

If you were there, who would you agree with?

[Guest]

Tho it's tempting - choose face numbers and probabilities.

No sums other than 2-12 only requires min[a]+min = 2 and max[a]+max = 12, allowing 0's 7's 8's, etc.

I want to check whether we're getting this right.

So, the dice don't have to appear to be normal six sided dice? While they both must have six sides, they can have any positive integer as long as it is not possible to roll a 0 and 1 or a 6 and 7 for example. Ie, if we have a 0 on one dice, there cannot be a 1 on the other, unless there is zero chance of it being rolled.

However, if we are assuming that if the dice are allowed to appear irregular, then are we assuming that the dice don't have to be six sided? And can they be attached to each other or do their rolls have to be independent of each other.

In regards to Ordover's last post, I don't think the question is carefully worded. Carefully worded puzzles tend to be quite short and succinct.

[bonanova]

Hey, question - is there someplace one can go for the actual answer to these? Or do I just have to listen to every episode of Car Talk?

Well you can go here for my answer. Post #15.

And read d3k3's answer here.

We're just prolonging the agony now by thinking about allowing numbers other than 1-6 on the faces.

And yes, the OP intends to say the dice are cubic, with the numbers 1-6 on each.

[bonanova]

Carefully worded puzzles tend to be quite short and succinct.

There is a "flavor" of puzzles that include "flavor text" which may contain clues.

Some people enjoy both writing and solving them.

Succinct version:

Is it [mathematically] possible to individually specify the face probabilities

of two cubic dice, not necessarily identically, each numbered 1-6, with the

effect that the sums 2-12 occur with equal [1/11] probability?

[Guest]

There is a "flavor" of puzzles that include "flavor text" which may contain clues.

Some people enjoy both writing and solving them.

Succinct version:

Is it [mathematically] possible to individually specify the face probabilities

of two cubic dice, not necessarily identically, each numbered 1-6, with the

effect that the sums 2-12 occur with equal [1/11] probability?

No, but the question as originally stated isn't mathematical - is it practical to load dice to create that result? I mean, clearly if the dice had an internal controlling mechanism, you could make them come up however you wanted them to.

[Guest]

Come to think of it, what's most unusual about the sequence of numbers rolled is that it does not include a seven - rolling a die 5 times and not comng up with the most common roll?