bonanova Posted December 22, 2008 Report Share Posted December 22, 2008 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? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted December 23, 2008 Report Share Posted December 23, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted December 23, 2008 Author Report Share Posted December 23, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted December 23, 2008 Author Report Share Posted December 23, 2008 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? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted December 23, 2008 Report Share Posted December 23, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted December 24, 2008 Report Share Posted December 24, 2008 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? Quote Link to comment Share on other sites More sharing options...
Question
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?
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