Welcome to the big leagues! I'll give you a chance to warm up with an easy one before you tackle the big boy.
Warm Up Question
I have three daughters and each has one brother. How many children do I have?
Question - The Big Boy
You have three dice, each with six sides, where the first will roll higher than the second more than half the time, the second will roll higher than the third more than half the time, and the third will roll higher than the first more than half the time. Additionally, when you roll all three, the expected value of their sum is 7. What numbers are on the faces of the three dice? Show your work.
If you get the answer to the big boy, PM me. If you're correct and you are the first one to answer correctly, you'll win a WSO t-shirt! Don't cheat, although I doubt it'll help you. This is a custom riddle I wrote personally. However, if you'd like to commiserate in the comments, that's fine, but be aware that you may be helping others. Your call.
Good Luck!
Warm up question: 4 children.
For the second question, I got an average expected value of 1.875 for dice A, 2.75 for dice B and 2.375 for dice C.
Yeah 4 is the first one. Working on the second, definitely tricky.
Getting thrown off by the "expected sum of 7" @mikesswimn
hint for others: rock - paper - scissors
Before I say 4 .... have the children been born yet? You don't 'have' anything until they are born imo.
4
Solved and sent for "rolls higher more often than lower", though not "more than half the time". Good enough?
Wasn't good enough ;-)
Sent in solution for the big one!
For the big one, some more information I've gotten for others to use. This is assuming I'm correct....
The dice are nontransitive.
The probability that the first rolls a higher number than the second, the probability that the second rolls higher than the third, and the probability that third rolls higher than first are 21/36, 21/36 and 25/36.
That's the maximum probability, but it's not the only solution. Technically for it to be a set of non-transitive dice they could all have the probability of 19/36 of being higher than the next.
Also, can you post up the solutions for everyone else after they have been solved. For the past weeks, I would like to see if I was correct because the show answer buttons won't work.
Are the sides of the die required to be integers between 1 and 6?
Damn, good job everyone! I've gotten some solutions in my inbox and while I haven't checked them out, I'm fairly confident (given the number of attachments) that we have a winner in there. I'll report back tomorrow morning after checking them in my own spreadsheet to declare the winner!
@yeahright Non-transitive dice, exactly what I'm talking about. Good work!!
@glide9811 No, the sides of the dice do not need to be integers between 1-6. In fact, they don't need to be A) integers, or B) positive.
@Skinnayyy Yes, this is true, but note Miwin's dice. Not 19/36 but still non-transitive.
Taking too long to realize this may have cost me the race...
It looks like we have a winner! At 12:34pm yesterday, @"Monkey in Acquisitions" got the big one correct!!
I'll post tonight how I came up with the question!
awe man! I wish I would have seen your message earlier than this morning!
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