Hannah finds two dice in the attic with a rather peculiar feature: they are not standard dice (which have every natural number between 1 and 6 exactly once), but on both there are six
certain (not necessarily different) non-zero natural numbers. Hannah notes that the probability distribution
the sum of the eyes of both dice is exactly the same as that of two standard dice.
For example, the probability of rolling a sum of 12 pips is equal to 1 . in both cases
36 .
What are all the possible pairs of dice that fit the description above? List them all and clearly explain why there cannot be others.
#statistics problem with dice
half crane
crude plinth
yeah i know, but i dont wanna be like the other students, they dont know programming
It's not a matter of programming or not, gotta understand the subject first
Which goes with probably doing it on paper first, before code
placid fog
You aren't going to be able to solve this by getting every combination and checking which ones meet the criteria
half crane
so i cant really understand this
placid fog
that's too many values
half crane
it wouldve been cool tho
placid fog
you have to actually find ways to reduce the sample size
half crane
you have to actually find ways to reduce the sample size
alr
placid fog
Meaning you'll have to do the math to know which heuristics to apply to your program
placid fog
I'm not actually sure
I'd have to think about this for a while
this is a difficult problem actually
half crane
ofc it is
but the thing is, my code would work
theoretically
ping me if you found anything
placid fog
I ran a different calculator that can handle bigger numbers. The number of combinations of two different dice containing all values 1 to 11 randomly is 3.2e7. That means there are a total number of possible rolls of about 1.03e15, which would take 935 terrabytes to store
The "Generate, Map, Filter, Reduce" pattern isn't going to work here. I think this is more puzzle than math
placid fog
I'm going to think about this while I get lunch. There's probably a way to reduce it
My gut instinct is that it's a trick question and the answer is literally just two dice of [1,2,3,4,5,6]
half crane
My gut instinct is that it's a trick question and the answer is literally just t...
no i have the solution
theres one solution
but for the math thing you need to find why
placid fog
Okay. So you need two dice with non standard numbers that nonetheless produce an identical probability curve as 2d6, right? That'd means that you'd need two dice whose expected values sum up to 7. So when checking your dice, you could filter the second list of dice to ones that have an expected value equal to 7-this die average
half crane
what is 2d6
where does it say it has to sum up to 7
i dont get that part
@placid fog
placid fog
what is 2d6
Nerd speak for two six sided dice
half crane
Nerd speak for two six sided dice
nerd?
placid fog
where does it say it has to sum up to 7
That's the only way to produce the same bell curve, the peak of probabilities must be 7
half crane
???????
placid fog
The most common number to roll on 2d6 is 7. If you have a different set of dice with the same probability breakdown, that means the most common number to roll on them must also be 7. That would be the sum of the average roll of both dice
half crane
Dungeons and Dragons
bro