## Poll

16 votes (50%) | |||

12 votes (37.5%) | |||

5 votes (15.62%) | |||

2 votes (6.25%) | |||

10 votes (31.25%) | |||

3 votes (9.37%) | |||

6 votes (18.75%) | |||

5 votes (15.62%) | |||

10 votes (31.25%) | |||

7 votes (21.87%) |

**32 members have voted**

December 26th, 2020 at 12:18:55 PM
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y = ln(x/m-as) / r^2

(r^2)y = ln(x/m-as)

e^((r^2)y) = x/m-as

me^(rry) = x-mas

(r^2)y = ln(x/m-as)

e^((r^2)y) = x/m-as

me^(rry) = x-mas

Last edited by: Ace2 on Dec 26, 2020

It’s all about making that GTA

December 26th, 2020 at 6:03:43 PM
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Quote:WizardQuote:chevy

My belated guess is

me^(rr y) = x-mas

Where does the natural log fit into it?

multiply both sides by r r gives rr y = ln(x/m-as)

exponential of both sides gives. e^(rr y) = e^ln(x/m-as) = x/m-as

multiply both sides by m gives. me^(rr y) = x-mas

December 27th, 2020 at 6:23:57 AM
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Quote:chevy

My belated guess is

me^(rr y) = x-mas

Correct! Sorry about the natural log question earlier.

It's not whether you win or lose; it's whether or not you had a good bet.

December 28th, 2020 at 9:08:27 AM
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I probably asked this one before years ago, but let's run it up the flagpole again.

Five pirates have a chest with 1,000 coins on their ship, which they wish to divide. Let's call the pirates, in rank order from highest to lowest, Adam, Bob, Chris, David, and Ernie. Here are the pirate rules on how to divide it:

1. Ernie makes a suggestion on how many coins each pirate gets. For example, Adam 400, Bob 200, Chris 100, David 50, Ernie 250.

2. All pirates vote on the suggestion.

3. If the vote gets a majority, then that is what they do and it's over.

4. If the vote does not get a majority, then they make Ernie walk the plank.

5. David, now the lowest in rank, makes a suggestion.

6. This process keeps repeating until a vote gets a majority.

Please note that a tied vote is not a majority and the pirate making that suggestion will walk the plank.

Each pirate has the following priorities, from highest to lowest.

1. Get get as many coins as possible.

2. To make other pirates walk the plank (pirates are bloodthirsty)

3. To live

What should Ernie suggest for the division?

Five pirates have a chest with 1,000 coins on their ship, which they wish to divide. Let's call the pirates, in rank order from highest to lowest, Adam, Bob, Chris, David, and Ernie. Here are the pirate rules on how to divide it:

1. Ernie makes a suggestion on how many coins each pirate gets. For example, Adam 400, Bob 200, Chris 100, David 50, Ernie 250.

2. All pirates vote on the suggestion.

3. If the vote gets a majority, then that is what they do and it's over.

4. If the vote does not get a majority, then they make Ernie walk the plank.

5. David, now the lowest in rank, makes a suggestion.

6. This process keeps repeating until a vote gets a majority.

Please note that a tied vote is not a majority and the pirate making that suggestion will walk the plank.

Each pirate has the following priorities, from highest to lowest.

1. Get get as many coins as possible.

2. To make other pirates walk the plank (pirates are bloodthirsty)

3. To live

What should Ernie suggest for the division?

It's not whether you win or lose; it's whether or not you had a good bet.

December 28th, 2020 at 5:52:18 PM
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Does anyone not understand what is being asked?

It's not whether you win or lose; it's whether or not you had a good bet.

December 28th, 2020 at 7:17:45 PM
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Quote:WizardDoes anyone not understand what is being asked?

I am somewhat unclear on the priorities. Does getting one coin mean that choice is better than making somebody walk the plank? (and getting coins assumes you actually live, thus I'm not sure how priority 3 enters into it)

If so I could venture the following guess

Looking at rounds in reverse order

4) If it gets down to Adam and Bob....Adam votes no and Bob walks the plank. Ends with A=1000

So Bob can't let it get to this, and must agree with Chris's offer unless he get's nothing in which case priority 2 kicks in and better to vote no and make Chris walk plank.

3) If it gets down to Adam, Bob, and Chris....If Chris walks, then Bob does in next round. So Chris would have to give Bob just enough incentive to vote yes allowing for his own greed. Chris would offer A=0, B=1, C=999. (Here is where 1 coin is enough?)

2) If it gets down to Adam, Bob, Chris, and David, ..... David would need 2 people to do better than the round 3. David would offer A=1, B=2, C=0, D=997

1) So Ernie needs 2 people to do better than round 2. Either

A=2, B=3, C=0, D=0, E=995

or

A=1, B=3, C=1, D=0, E=995

or

A=2, B=2, C=1, D=0, E=995

December 28th, 2020 at 7:30:56 PM
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Quote:chevyI am somewhat unclear on the priorities. Does getting one coin mean that choice is better than making somebody walk the plank? (and getting coins assumes you actually live, thus I'm not sure how priority 3 enters into it)

If you walk the plank, your suggestion was rejected, so it's impossible to walk the plank with coins. You walk it with nothing.

While pirates are bloodthirsty, greed takes priority. They would rather get one coin than zero. If a pirate would get zero coins either way, he would sacrifice his own life to see an extra pirate walk the plank.

That all said, your answer is close, but there is a way for Ernie to get even more coins.

It's not whether you win or lose; it's whether or not you had a good bet.

December 28th, 2020 at 7:59:51 PM
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I guess Ernie only needs 2 voters to do better and the others can be cut out.

So. A=2, B=0, C=1, D=0, E=997

December 28th, 2020 at 9:01:33 PM
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Quote:chevy

I guess Ernie only needs 2 voters to do better and the others can be cut out.

So. A=2, B=0, C=1, D=0, E=997

Ding, ding, ding!!! You are correct, sir!

It's not whether you win or lose; it's whether or not you had a good bet.

December 29th, 2020 at 6:29:00 AM
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If I were Adam or Chris in this situation, I would vote against it, knowing that Bob and Dave for sure will vote against it. Then Ernie walks the plank, and they have a better chance of more coins. Seems to satisfy the requirements, yes?