Math Is Fun Forum

I say 2.

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

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.

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.

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.

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.

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.

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.

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.

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.

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?

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.