kk got it

Wow, pirates are dicks.

I still cant figure the 5 hate one :(

hat*

wait wait. White hats are somewhat visible even in the darkness, so... Cheating? Yeah. I didn't think so. Too bad.

no, no. its total darkness.

kk well im goin to sleep, if you wanna i can pm the answer, or i can give you guys some time to mull it over and post it tommorow

I'll think about it a little more.

I got it (looked it up). That one is convoluted as fuck.

I liked it though. yaks already gave you a great hint that is easy to overlook. The King promised a FAIR contest.

Damn, I am stupid. It should have been so obvious! If it is a fair contest, all of them get black hats, so that they all have the same chance of getting it right.

Right.

But do you know why you're right? Why wouldn't the King give 2 white and 1 black hat? Why wouldn't he give 2 black and 1 white?

And I wouldn't say you're stupid for not getting that - its easy to overlook if you don't realize the king cares that its fair. He certainly hasn't cared in any of these other scenarios :)

I'm not arguing with Hydro's one but really if I was logical and greedy I would vote no in this 5 way proposal (99,0,1,0,1) as a warning (if I was pirate number 5), this is on the basis that you can have the same offer after two more die, since the highest pirate cares more about survival then money they will perhaps, being logical, give in to your demands of a higher offer. Then the fact you want others to die means as number 5 it is better to accept the deal with less people involved...

Because it is a fair contest. If the hats were mixed, a logician or other would have a greater chance of getting it right.

@Soc, this would work, except that it relies on #4 declining the sharing of #2 on the same ground. Which he wouldn't do, because then pirate #3 would give him nothing, and #5 would accept THAT because if #3 dies, #4 does whatever he wants.

and with four left there is no reason for pirate number 1 (formerly number 2) to pick pirate number 3 (formerly number 4) over pirate number 4 (formerly number 5)?

To be safe you should accept the offer, but I thought they valued survival more? I dunno right I'm sure, logically the answer is sound, I just don't like the answer :P

There is a reason: If #4 decides he is screwed anyway, and #5 decides he gets a coin anyway, they both vote to kill #2 based on them being bloodthristy. (I am using their original numbers.)

The answer is really unintuitive. It relies both on survival>greed>killing and (even more importantly) that _all the pirates know that the other pirates think this way too_.

@Yellowjacket: Am I right or should I search for another answer?

You are right, but I think maybe for an incomplete reason. There is no chance involved.

All 3 logicians are brilliant, and they know it must be a fair contest.

A fair king would never pick 2 white hats and a black hat, because whoever saw two white hats would immediately know he's wearing black.

A fair king would also never pick 2 black hats and one white hat, because two logicians would see both a black and a white hat, and since they know from above the king wouldn't go two white and a black, then they each must be wearing black. They have an advantage over the 3rd man in the white hat, who, seeing 2 black hats, still has no certainty.

In fact, if the man in the white hat was the fastest thinker, and knowing the king is supposed to be fair, and thus would never pick 2/1 or 1/2, he would say with certainty then that he must be wearing black, and be wrong, which rejects the premise of the fair contest (the best logician is punished rather than rewarded).

The only way to be totally fair is to have everybody in a black hat - then its just whoever figures out the above points fastest wins.

**************************************************************
this one is just bastardly, I would never figure it out but props if any of you can without looking it up
***********************************************************

The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?

@YJ:

Do the prisoners know when the room is visited? Obviously they can't know by whom, or the whole point is defeated, but will they learn if a prisoner has visited the room and flipped a switch?

Ooh, looks hard. Impossible, actually. :) Give us time. PE: I'd guess no, though I'm of course not sure.

I figured it out... Won't spoil it, though.

@ President Eden.

I don't think anyone else besides the Warden and escorted prisoner know when someone is in the switchroom.

.Yeah, I've got it too. I'll wait for the rest of you though.

@ghug - The fly can't alternate speeds. It is stated in the initial riddle that he moves slower than the spiders. So even with a change of spped he couldn't avoid their triangular loops eventually catching him, but if he can stop, I have to rethink it.