A Tuesday Puzzle

5/3/11, 9:22 PM #1

Dan Donaldson
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A Tuesday Puzzle

Dan Donaldson

Here is one for you:

You have 4 dice with the following numbers on them:

3,3,3,3,3,3

2,2,2,2,6,6

1,1,1,5,5,5

4,4,4,4,0,0

your challenges is to choose one of the dice, and then I will take another. We will roll our dice together, trying to get the highest roll, and the winner is the one who rolls the best out of ten. Which die should you choose?

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: A Tuesday Puzzle

5/4/11, 1:13 AM #2

John Veerkamp
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Re: A Tuesday Puzzle

John Veerkamp

222266

Re: A Tuesday Puzzle

5/4/11, 3:11 AM #3

Dan Donaldson
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Re: A Tuesday Puzzle

Dan Donaldson

maybe, but maybe not. What is your rationale?

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: A Tuesday Puzzle

5/4/11, 6:14 AM #4

Alex Y
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Re: A Tuesday Puzzle

Alex Y

Any of them. You'll only win 1/3 of the time w/ a good opponent.

Re: A Tuesday Puzzle

5/4/11, 7:16 AM #5

Dan Donaldson
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;(

Dan Donaldson

Statistically, with two of the dice, I can pick one to win best out of ten consistently. Which one is the "best"?

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: A Tuesday Puzzle

5/4/11, 7:18 AM #6

Dan Donaldson
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Actually, I can pick one that will beat you.

Dan Donaldson

There is a hint buried in this answer

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: A Tuesday Puzzle

5/4/11, 12:10 PM #7

Larry Barrett
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Re: ;(

Larry Barrett

I think 2 is "best" in sense of having highest probability of winning against the other die. But Alex is correct in saying that for any die that you pick, I can select one that has a probability = 2/3 of winning against you on one roll of the dice.

1 wins against 2 with Prob=2/3, against 3 with P=1/2, against 4 with P=1/3

2 wins against 1 with P=1/3, against 3 with P=2/3, against 4 with P=5/9

3 wins against 1 with P=1/2, against 2 with P=1/3, against 4 with P=2/3

4 wins against 1 with P=2/3, against 2 with P=4/9, against 3 with P=1/3

Re: A Tuesday Puzzle

5/4/11, 2:14 PM #8

Alex Y
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Those are the probs I got as well

Alex Y

And since the second person gets to pick another die (as I read the puzzle, at least), I'll stick with my "it doesn't matter" answer. I agree that if the second person takes another die at random, 2 is the best die to start with, giving you slightly better than 50-50 odds, 14/27 chance of winning if I calculated correctly.

Re: A Tuesday Puzzle

5/4/11, 3:48 PM #9

Ed in Leaside
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4 ...

Re: A Tuesday Puzzle

5/4/11, 6:02 PM #10

Dan Donaldson
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Re: Those are the probs I got as well

Dan Donaldson

Sorry Alex, I misread your answer. You are correct. This is kind of a trick question kind of like the rock, paper , scissors game. For any choice, there is another choice with a higher probability.

- - -

I have been woodworking for about 25 years now, and would consider myself an enthusiastic amateur. My claim to fame (or infamy) has always been fixing stuff. I spent time in the Air Force in the 60's then went to work as an electronic technician for civil service. I finally got my EE, and being fed up with the civil service nonsense, took a job with Ford Motor Company until I went with the split to Visteon last year. I got interested in music and started playing in a bluegrass band. I wanted a new guitar, and that kind of led me into woodworking. I bought some books, a few tools, and built a guitar. Luckily, I didn't know any better than to try that as a first ever project. I still play it when I get a chance, so it must not be too bad if it can live for over 20 years. After a stint in Mexico for my job, I moved into a new house and built a small shop. Since then I have been collecting tools and skills, probably more of the former than the latter ;-). Finding this site has done more for my skills and enjoyment than anything else. I have learned a lot and really enjoy the friendships that I have made here. I have been married to LOML (Lori) for 32 years now and have 6 kids. When they are all gone, I want to get a 1 bedroom house (so there is not room for them to move back in) and at least a 6 car heated/air conditioned garage for a shop. (Dream on...)

Re: A Tuesday Puzzle

5/4/11, 6:18 PM #11

Alex Y
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Re: Those are the probs I got as well

Alex Y

No problem. My answer was rather cryptic, as I was trying to type it out fast on my phone before having to turn it off for a red-eye flight.

This is interesting, taking me back to sophomore abstract algebra. You expect a relationship like "is more probable than" to be transitive, but the relationship here is not transitive.

A Tuesday Puzzle

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