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#2 Re: Puzzles and Games » FUN math puzzles! » 2013-04-22 14:47:17

mathgogocart wrote:

Bobbym-1725-:)
50 P-awesome
100 P-Epic
200-Genius
400-Silver Medal
700-Listing Pro
900-Braniac
1500-
________________________________
1.Detective Wesley carefully examined the scene before him. He was in a hotel room about 3 miles from the victim's home. The victim's body lay in front of him peacefully on the bed. It was January 7th, 3:15 PM, the body was discovered by a hotel maid. The man's name was Sean Donovin. He was in his late twenties, a successful business owner, a Sunday school teacher, and was soon to be married. The detective shook his head in disgust. He whispered to himself, "Why would anyone commit suicide when they had everything going for them?"

The detective saw this as suspicious. The only potential suspects would have to be people he trusted. According to testimony from his coworkers and friends, he only trusted 3 people: his sister, Hannah, who was very close with the victim and who often assisted him while he taught at the local church; his brother, John, who owned a smaller, semi-successful business; and his fiance, Jenna.

The apparent cause of death was by injection of poison. At least his death was peaceful, the detective thought. The detective continued to search the hotel room, when he stumbled upon a suicide note. It read:

Jan 04/2009 4:10 AM

My loved ones,

Jenna, Sis, John, I would just like to tell you how sorry I am. Blame God for why I am to die today. Blame Him. Seek Him if you want to know why I did leave you. Do not mourn my death. Please move on.

Goodbye,

Sean


The detective saw this letter as somewhat suspicious. His last words were abrupt, almost impersonal. Why would a Sunday school teacher blame God?

The body was taken in for medical examination. Days later, the coroner would determine that the body died from a poison which killed instantly. The coroner would also determine that the body was only dead a mere 3 hours before it was discovered.

The detective then realized that the date and time used on the note were completely false. All 3 of those mentioned in the letter agreed the handwriting was indeed Sean's.

The detective realized that the identity of the murderer was given inside the suicide note. After a thorough examination of the note, Detective Wesley quickly arrested the murderer.

Who was it?-??100 points

I believe I have it:

#4 Re: Puzzles and Games » Can U solve this? » 2013-04-22 08:50:04

julianthemath wrote:

up

New edition :

P * C.P = 5

P = Prime
C = Composite

Still not possible. 

All P are such that P > 1. The smallest P is 2. And, the smallest C such that C > 0 is 4

Thus P * C.P >= 2 * 4.d = 8.0 + 2d (where 2d is 2 times the decimal part)

If you were trying to go for 2 * 2.5, then the 2 in 2.5 is not Composite, it is Prime.

#5 Re: Puzzles and Games » Nehushtan’s challenge problems » 2013-04-15 11:54:55

Case 1: (same proof as my original answer)
assume x > 0
then, since x<=y<=z, and x > 0, then y > 0 and z > 0
Y >= x, and xz <= yz
and, xz <= yz + xy
thus xz <= xy + yz

Case 2:
assume x = 0,
then, since x<=y<=z, and x = 0, then y >= 0 and z >= 0
xz = 0, xy = 0, and yz >= 0
thus xz <= xy + yz

Case 3:
Assume y = 0,
then, since x<=y<=z, and y = 0, then x <= 0 and z >= 0
thus xz <= 0, xy = 0, and yz = 0
thus, xz <= xy + yz

Case 4:
Assume z = 0,
then, since x<=y<=z, and z = 0, then x <= 0 and y <= 0
xz = 0, xy >= 0, and yz = 0
thus, xz <= xy + yz

Case 5:
Assume z < 0,
then, since x<=y<=z, and z < 0, then x < 0 and y < 0
xz > 0, xy > 0, and yz > 0, (all are positive numbers)
since |x| >= |y| >= |z|
xy >= xz >= yz

Thus, xz <= xy
and, xz <= xy + yz

#6 Re: Puzzles and Games » Nehushtan’s challenge problems » 2013-04-15 08:28:33

x <= y <= z implies Y >= x

thus xz <= yz

and  xz <= yz + xy

thus xz <= xy + yz

#7 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 20:32:14

Here is what you refuse to consider, but it is right there:

Pretend that I was just Eddie.  I have reasoned this out for myself.  I have shown how this puzzle will go.  I don't need to consider what will happen in step 3 because I won't let it get that far.

I am not going to get stuck with just one coin.

I will accept Alex's proposal if he makes the correct one. 

Now, I am Billy.  I too have reasoned this out.  I will also accept Alex's proposal if he makes the correct one.

Now, I am Alex.  I will die if I don't get this right.  I don't have a death wish.  I have just reasoned this out.  I will offer Billy 50 and Eddie 50.

For if I don't, I will die.

My only rational decision is to make the best offer I can to save my life.

If I was Eddie, I too would extort the maximum that I could get from Alex
If I was Billy, I too would extort the maximum that I could get from Alex

I am Alex and I have no choice but to offer each of them 50, because I I'll die if I don't.  Heck, if I was them, I'd kill me too if I didn't offer them each 50.

That's just how it goes.  At least I'll still have my life.

#8 Re: Puzzles and Games » 5 Pirates Puzzles » 2013-04-13 18:52:04

MathsIsFun wrote:

I have made TWO versions of this puzzle (used to have just one).

One where the voting is done by all Pirates:
The other where the voting is done by all Pirates except the oldest:

Have a go at the puzzles and let me know if you agree with the solution provided.

I gave this a go, and my proposed solutions is under another post titled:

"5 Pirates Solution is wrong - here is the real solution"  created on 4-13-2013

Since I'm new, I don't know how to put a link to that post in this message.

But, I thought I would post this here since this post is what encouraged me to actually post my proposed solution on the forum.

I had to remove the links in the reply to get this posted.

#9 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 18:30:45

mathdad wrote:

And likewise, why is it rational?  Why does the definition of the word "rational" change because we are in the context of a puzzle?

Nehushtan wrote:

It is rational because accepting 1 gold is better than accepting none.

You have once again changed the definition of rational for the puzzle's sake.  Offering one gold in Collin's position is not a rational means of saving one's life when confronted with bloodthirsty pirates.


mathdad wrote:

Are you saying that Eddie is greedy by accepting 1 gold coin?  Is that greedy?

Nehushtan wrote:

Yes. Why shouldn’t it be?

Because you have changed the definition of greed for your own sake again.  The definition of greed should not change because we are in the context of a puzzle.


mathdad wrote:

And, tell me, by the parameters in the puzzle, how you can say that Eddie's "greed" of accepting 1 gold coin will outweigh his bloodthirstiness?

Nehushtan wrote:

And what has that got to do with the puzzle? Here you go making up more of your own stuff!

Again, the puzzle set the stage, and the pirates are described as bloodthirsty.  You have chosen to ignore what has been stated in the puzzle.  If the pirates are not bloodthirsty, then explain why Collin must offer Eddie 1 Gold?  Without the pirates being bloodthirsty, then there in no reason for Collin to offer even 1 Gold to Eddie.  Collin should be able to keep all 100 for himself by your logic.

anonimnystefy wrote:

I don't know if I would call the things he said namecalling, but they do seem a bit harsh. I am sure it was unintentional.

Nehushtan wrote:

Not as harsh as the arrogance of some people, strutting into a forum as a complete newbie and stranger and declaring: “Look here: you’re wrong, I’m right!”

Arrogance has nothing to do with it.  I wanted the opportunity to debate the solution with like minded individuals.  The title was chosen to stimulate intelligent debate.  If you see me as arrogant, and are offended, then you are in control of your own destiny.  You can choose to ignore my post and move on.  Yet you stay here, because it seems you want to start a fight of some sort.

Now, the name calling has begun, you called me arrogant.  I will not fight with you, and name calling on an online forum is useless.

You are dead set on disagreeing with me despite what is rational, intelligent and logical in the context of this puzzle because you are angry with me for some reason.

I enjoy logic puzzles, that is why I came here.  Finding the solutions and considering the problems stimulates my brain - I find it fun.

The fact that I am a newb, and haven't posted before is irrelevant.  What - newbs can't have fun without paying homage to the elders?

The solution to this puzzle had a link offering the ability to "discuss the solution" on the forum.  That is all I did, and all I wanted.

I guess I'm done for now.  This is no longer any fun.

#10 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 17:49:36

anonimnystefy wrote:

I don't know if I would call the things he said namecalling, but they do seem a bit harsh. I am sure it was unintentional.

I agree, there was no name calling, other than what was implied by the statement.  I guess I found it easy to infer what he was implying.  Perhaps I misinterpreted his meaning.

#11 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 17:30:38

Nehushtan wrote:
mathdad wrote:

Again, it says that the pirates are rational and intelligent.  No specific definitions of those words were given.  We all know that in real life, it would be completely irrational to offer 1 gold coin in that position and expect a greedy, bloodthirsty pirate to accept the offer.

Why is it irrational IN A PUZZLE to have a pirate accept 1 gold because otherwise he would have nothing at all? If this situation offends your sensibility, you can always assume that later on, the pirate having the most gold gets murdered in his sleep, the other pirates start squabbling over the gold, etc. Do what you like with your imagination outside the puzzle. However, when you are in the puzzle itself, you go by the rules of the puzzle. You don’t go making up your own.

And likewise, why is it rational?  Why does the definition of the word "rational" change because we are in the context of a puzzle?  The puzzle set the stage, and the pirates are described as bloodthirsty and greedy.  Are you saying that Eddie is greedy by accepting 1 gold coin?  Is that greedy?  Who would agree that this is greedy?  Colin is being greedy.  What allows for Collin to be more greedy than Eddie in this puzzle?  Answer that.

And, tell me, by the parameters in the puzzle, how you can say that Eddie's "greed" of accepting 1 gold coin will outweigh his bloodthirstiness?  The puzzle doesn't define those limits, or what weighs more than the other.  You can't assume that the bloodthirstiness will be appeased by 1 gold coin.  The maximum limit we have here is 100 gold coins, and if it is at all possible in the puzzle to appease the bloodthirstiness, then we have no other data, other than 100 Gold to go with.  Thus, if Collin wants to appease Eddie's bloodthirstiness, he must offer his maximum to appease it.  That maximum is 100 Gold.

#12 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 17:20:02

anonimnystefy wrote:

There is no namecalling.

You should understand that the rules of the problem must be followed and not your opinion.

I wasn't referring to you, but the other guy who said that I didn't understand and was making stuff up.

#13 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 16:57:39

And, the ONLY rational, intelligent thing to do in that position would be to fight for your life, and make the absolute best offer possible.  And, that would be for Collin to offer Eddie 100 gold, and save his life.  Making intelligent, rational decisions about saving your life is a parameter of the puzzle.  I believe I understand the parameters.  What would any rational, intelligent person do in this situation?

Again, we are still debating - there is no need to start the name calling.  Keep the debate on the puzzle.

#14 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 16:46:04

Nehushtan wrote:
mathdad wrote:

Again, it is irrational to assume that a greedy, bloodthirsty pirate would accept 1 gold coin.
It is also irrational to assume that you would live with such a pittance.

This is NOT stated in the puzzle. This is something you made up yourself. When you play a game, you follow the rules of the game. You DO NOT make up your own rules! shame

Here is the URL of the puzzle:
OK, URL not allowed.....

w-w-w-.-m-a-t-h-I-s-f-u-n-.-c-o-m-/-p-u-z-z-l-e-s-/-5---p-I-r-a-t-e-s-.-h-t-m-l

Again, it says that the pirates are rational and intelligent.  No specific definitions of those words were given.  We all know that in real life, it would be completely irrational to offer 1 gold coin in that position and expect a greedy, bloodthirsty pirate to accept the offer.

#15 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 16:30:50

Is has been my contention from the start that case 3 doesn't matter, because the puzzle starts and ends at case 5.

But, if we consider case 3, Eddie must not accept 1 coin at case 5.

That will take us to step 4, or another solution at case 5 exists.

Either way, the official solutions is still in question.

Step 3 depends on what happens in case 5, and if it goes past that, case 4., .....

I don't agree that it is rational or intelligent to believe that an offer of 1 coin is suitable for guaranteeing that you will stay alive.  Again, parameters of the puzzle.

#16 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 16:18:18

Again, the puzzle starts with 5 pirates, not 3.  Case 3 is irrelevant.

Case 5 does NOT depend on case 3.  Case 5 comes first.

Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?


Again, it is irrational to assume that a greedy, bloodthirsty pirate would accept 1 gold coin.
It is also irrational to assume that you would live with such a pittance.

And

"As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard."

This line here allows each pirate to calculate what will happen in future dealings. 

And so, if you propose that Alex can offer 98 for himself, 1 for Collin, and 1 for Eddie (This is THE official solution posted on this site......), then tell me, by what is written in the previous quote "if a pirate would get the same number of coins if he voted for or against a proposal, he will vote AGAINST....."  means?

It means that Eddie must vote AGAINST receiving 1 coin, because that is what you are offering in step 3 - just a single coin to Eddie.

This is NOT allowed by the puzzle, you MUST vote to not accept the official solution to the problem, and kill the pirate Alex.

#17 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 16:01:19

anonimnystefy wrote:

It is not.

We need to dicuss the 3 case first, otherwise there is no way we can come to an agreement on 5.

Let's say that Collin still proposes the 99:0:1 deal. What is Eddie supposed to do?

You have missed a step.

First:  Colin must maximize his profits AND stay alive.  He is not psychic and can't say what any other pirate will do.  He must guarantee that he stays alive as his first priority. Secondary, he must try to gain gold for himself.

Second:  Eddie must make a decision depending on Colin's proposal.


Thus, what proposal MUST Colin make?

#18 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 15:46:37

Not true, the parameters of the puzzle are to maximize your profits and stay alive.

But, this is all moot anyway, because case 3 never ever comes into play.

No pirates die, and Alex offers both Billy and Eddie each 50 gold coins.  They accept the offer.

That is the solution.

#19 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 15:38:58

The parameters of the puzzle are not only to maximize your profits, but to stay alive as well.

What you need to consider (as Colin) are your possible outcomes:

1. you die, and Duncan gets all the gold.

2. you live, and Eddie gets all the gold.

Either way, you get no gold.  Your only decision here is whether you want to live or die.

Put yourself into the problem, and pretend it is real.  What would you really do?

I can guarantee that nobody would propose offering Eddie 1 coin.

Would you die just to keep me from getting gold?  You can't take it with you.

Seriously?  You wouldn't even consider offering Eddie even 2 coins? 10?

The reality is that you would offer Eddie all the gold, your sword, and the clothes off your back.

I didn't write the puzzle.  I am only operating within what is written.

#20 Re: Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 15:13:10

anonimnystefy wrote:

Let's talk about the 3 case first, because that is where the disagreement begins.

If you were Eddie and I was Collin, and I proposed to you the 99:0:1 deal, would you accept (knowing that you will get nothing if I die)?

No I wouldn't, because as Eddie, I know I am in control and can do much better for myself.  Let me pose this question to you:

You a making a proposal to me and to one other person.  You know full well that the other person will kill you regardless of what you propose.  Knowing full well that you are going to die if you don't make me happy, would you still propose to offer me only 1 coin, keeping 99 for yourself?  Realize of course that you only have one opportunity to make me happy before you die.  Also realize that I am a bloodthirsty,greedy pirate who kills and steals for a living.  And, that for 1 measly coin, I would probably rather see you die for your insulting offer?  And, realize that you can't take the gold with you if you are dead.  Your life is entirely in my hands, and you propose that I should only get 1 coin and you get to keep 99 for sparing your life?

#21 Puzzles and Games » 5 Pirates Solution is wrong - here is the real solution » 2013-04-13 13:57:18

mathdad
Replies: 30

This is for the version where all pirates get to vote:

Forum Solution:
The oldest pirate will propose a 98 : 0 : 1 : 0 : 1 split, in other words the oldest pirate gets 98 coins, the middle pirate gets 1 coin and the youngest gets 1 coin.

Let us name the pirates (from oldest to youngest): Alex, Billy, Colin, Duncan and Eddie.

Working backwards:

2 Pirates: Duncan splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.

3 Pirates: Colin splits the coins 99 : 0 : 1. Eddie will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing.

-    Incorrect.  Eddie will not accept the deal.  This is not about gold.  Instead, it is about life and death.  Who is really in control here?  The premise is that Colin is in control at this point, and can be greedy by offering Eddie just a single gold coin.  But, the reality is that Colin’s life is in jeopardy.  If Colin doesn’t please Eddie, he will die.  Eddie knows this, and he will not settle for just 1 coin.  Eddie is in complete control and will extort Colin to the fullest extent possible.  In fact, since pirates are bloodthirsty and greedy, Colin had better offer Eddie all the gold, or Eddie will vote against his proposal and he will die.  What good is all the gold in the world if you are dead?  Thus, to save his own life, the only proposal he can make is to give all the gold away.  And, since it is Colin’s proposal, Colin must vote in favor of it, because Duncan will definitely vote no, having been offered nothing.  Eddie, now having 100% of the gold will also, finally, vote in favor of it.  If Eddie votes no, then he will get nothing from Duncan’s proposal when only 2 pirates remain.

-    Poor Colin is thinking hard about his dilemma.  Maybe he can strike a deal with Duncan instead.  Colin’s only recourse is to offer Duncan all the gold instead of Eddie.  But, that also will not work.  While Duncan would get 100% of the gold here, he will still vote against it in favor of killing off Colin.  Once Colin is gone, he gets all the gold anyway due to the 2 Pirates remaining rule.  Thus, Colin must offer all 100 coins to Eddie, and Colin must accept his own deal or he will die.

4 Pirates: Poor Billy is in the same boat.  He will die unless someone besides him accepts his proposal.  What can he do?

Billy can’t offer it to Eddie, because Eddie will get the same proposal from Colin after Billy is gone.  Eddie would vote against Billy in this case, even if Billy offered him all the gold, in favor of killing him off.  Eddie would stand to get all the gold all the time with Billy gone.

That leaves Duncan and Colin.

Make no mistake.  The pirates are greedy and bloodthirsty.  Billy must offer all the gold to one of them of he will die.  It doesn’t matter which one he chooses.  He must only please one of them, and accept his own proposal.  Assuming that there will be future spoils to share, his best strategy would be to alternate between the two pirates each time there is gold to be split.

5 Pirates:  Alex must have 3 votes in acceptance of his proposal or he will die.  Obviously, he will vote for his own proposal, but can he get the other 2?

Duncan and Colin are better off with Alex gone (which would force Billy to select one of them to receive all the gold).  Due to their thirst for blood and greed, they would opt for seeing Alex die and having a 1 in 2 chance of getting all the gold.  They would not accept anything short of 100% of the gold from Alex.  However, if Alex offers 100% of the gold to only 1 other pirate, he will only have 2 acceptance votes (his own, and the pirate receiving all 100 gold coins).  Thus, Alex cannot make a deal with either of these two.

That leaves Billy and Eddie.  Alex must give part of the gold to each, and have each of them accept the proposal.  Is that possible?

Billy knows that if he demands 100% of the gold for himself, then he would get nothing because Eddie would not accept, and Alex would die.  And, if Alex dies, then we have to drop to the 4 Pirates solution.  In the four pirates solution, neither Billy nor Eddie gets anything.

From Eddie’s perspective, he also knows that he gets nothing from having Alex die.  Billy is in no danger, and has a solution for staying alive in the four pirates solution.

Both Billy and Eddie have the power to accept or reject Alex’s proposal.  They both need the other to accept the proposal to get paid.  If either of them rejects the proposal, then neither of them will get anything.  Their positions are equal, and Alex has only one thing that he can do.  Offer each of Billy and Eddie 50 gold coins.

Thus, the final solution is 0-50-0-0-50.

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