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1 vote (16.66%)
1 vote (16.66%)
1 vote (16.66%)
4 votes (66.66%)
1 vote (16.66%)
1 vote (16.66%)

6 members have voted

Wizard
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Wizard
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March 20th, 2020 at 2:24:35 PM permalink
I know this one is similar to the Ace2 variant of the light bulb puzzle, but I'm finding what Ace2 brought to the table very interesting.

You have a single fair six-sided die. You keep rolling it until you've rolled each side at least twice.

Question 1: What is the average number of rolls needed?
Question 2: Put the solution in a closed form expression (warning -- difficult -- I think).

Usual rules apply. If you're already a member of the beer club and can't restrain yourself for 24 hours, feel free to PM me.

Last edited by: Wizard on Mar 20, 2020
It's not whether you win or lose; it's whether or not you had a good bet.
ssho88
ssho88
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March 20th, 2020 at 5:50:15 PM permalink
I think you should change it to ..... until you've rolled each side AT LEAST twice
Wizard
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Wizard
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March 20th, 2020 at 8:24:25 PM permalink
Quote: ssho88

I think you should change it to ..... until you've rolled each side AT LEAST twice



Good point. I just made that edit. I think we need to let the 24-hour clock run out before the fun can begin.
It's not whether you win or lose; it's whether or not you had a good bet.
EdCollins
EdCollins
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March 20th, 2020 at 10:02:40 PM permalink
I'm not looking for a beer, but for Question 1, I think the average number of rolls needed is 28.165.
I have no idea regarding Question 2.
Suited89
Suited89
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March 20th, 2020 at 10:24:10 PM permalink
If at least twice I estimated the puzzle as

28 + 1/6 as n*((2n+1)/n)^2 where n is 6 sides of the die.
some people need to reimagine their thinking
Klopp
Klopp
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March 21st, 2020 at 3:27:31 AM permalink
I am not looking for a beer either, but I think the answer to question 1 is 24.134
ssho88
ssho88
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March 21st, 2020 at 3:59:23 AM permalink
Quote: Klopp

I am not looking for a beer either, but I think the answer to question 1 is 24.134



Agreed. I got the same answer( through a not so intellectual method)
Wizard
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Wizard
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March 21st, 2020 at 5:31:27 AM permalink
Quote: EdCollins

I'm not looking for a beer, but for Question 1, I think the average number of rolls needed is 28.165.
I have no idea regarding Question 2.



I disagree on question 1, but you're in the ballpark
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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March 21st, 2020 at 5:33:54 AM permalink
Quote: Suited89

If at least twice I estimated the puzzle as

28 + 1/6 as n*((2n+1)/n)^2 where n is 6 sides of the die.



Let's see, where's my calculator...

That comes out to 56.166666, which is way too many.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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March 21st, 2020 at 5:35:21 AM permalink
Quote: Klopp

I am not looking for a beer either, but I think the answer to question 1 is 24.134



I agree.

To get the beer, one must show his work. I'll award two beers for this one, one for each part.

Also, please put answers and solutions in spoiler tags next time.
It's not whether you win or lose; it's whether or not you had a good bet.

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