00:00Today we are going to solve a single riddle, but I promise you that it will make your brain work like never before.
00:07Should we start?
00:10So the principle is simple. There is a secret island held by a crew of pirates as their base.
00:16The crew consists of 5 pirates, and they have just returned with a chest full of gold coins.
00:22When they count their catches, it turns out that there are exactly 100 coins.
00:26Now, they are about to distribute them among themselves.
00:29You would say that 20 coins for each pirate should be fair, right?
00:33But let's not forget the hierarchy. Some pirates are stronger than others, and those who are weaker must obey those who are stronger.
00:41Let's give them names so as not to be confused.
00:44Arnie is the strongest. The second is Bernie. Then comes Connie. The fourth is Donnie. And the weakest is Ernie.
00:52You can memorize them by the first letters of their names, to simplify.
00:56By the way, pirates have strict and rather fair rules to share the treasure.
01:01The strongest pirate offers a share, and the rest of them must vote for or against the offer.
01:07The simple majority wins, and if 3 pirates or more vote for the offer, they share the loot as agreed.
01:15But if more pirates vote against it, then the one who offered the share leaves in order to never return.
01:24Then, the pirates remain voting again, using the same rules.
01:31If there is an equality, however, then the pirate who offered the share has an additional way to break the equality.
01:39All the crewmates are also very greedy, and none of them will miss an opportunity to get as many gold coins as they can.
01:47I should add that pirates are reasonable guys. None of them wants to leave the crew forever and lose the potential benefits of subsequent adventures.
01:56They therefore first care about their stay with the crew, and the treasure in the last place.
02:01In addition, if a pirate does not care about his vote in terms of money, he will vote against the share.
02:07It is because he wants to get rid of the strongest opponents naturally.
02:12Another thing to know about pirates is that they all like to look at the back of their strongest comrades when they leave.
02:19But if they have the choice between getting rid of a rival and even taking a single piece of loot, they will choose the liquid money each time.
02:27In the last place, the pieces cannot be cut into pieces or divided in any way.
02:34Pirates cannot arrange to share the pieces or foment a sneaky plot against their strongest companion to guarantee victory.
02:42This is not an arbitrary rule. They just do not trust each other enough to respect the arrangements.
02:48Each pirate can only count on himself. Yet, they are all rational, and each pirate knows that the other guys are also rational.
02:58They will use a rigorous logic to get the best out of their situation.
03:02Now, the big question. How can they divide the gold in such a way that none of the pirates leave?
03:08I'll give you a clue. There seems to be no trust between the crew members.
03:14And that could well be the key to the solution.
03:17Pause the video now to think, or look further if you want to see the answer right away.
03:28The solution
03:32Ready? Then let's continue to explain.
03:35To find the solution, we must think well ahead and go back from the last remaining pirate.
03:42Let's say that Ernie is now the only member of the remaining crew, and that he has recovered all the gold for himself.
03:49How did he do that? Well, he had to eliminate the four others, of course.
03:54Let's go back a little. There is only Donnie and Ernie left, with Donnie offering the share.
04:00If he says that he will take all the gold for himself, Ernie will want it.
04:04Naturally, he will vote against such an unfair share, and the same thing will happen in all other cases, unless Donnie offers him at least 50 gold pieces.
04:14We remember that the pirates are greedy, so Donnie will not do such a stupid thing.
04:19If Ernie is in disagreement, they will have an equality at 1 to 1, and Donnie will have the majority vote, which will leave him all the gold and nothing for Ernie.
04:28Now, another step back, and we have Connie back on the bridge, and who offers a division, since he is now the strongest of the left behind.
04:37This time, if Connie decides to seize all the money, even her decisive vote will not help her.
04:42There will be two votes against his only vote, and he will have to take the miserable path.
04:47For things to work for him, however, Connie must get a vote.
04:53For this, he can offer a single piece to one of the remaining pirates.
04:57If he tries to buy Donnie's vote, Donnie will still vote against the share.
05:02Why? Because he knows that if Connie leaves, he will get all the money instead.
05:07So, it is not in Donnie's best interest to be bought at such a good price.
05:12Ernie, on the other hand, is the same thing. He gets nothing anyway.
05:16So why vote for Connie's proposal?
05:19But if Connie offers him a single piece for his vote, he will be better off than with any other result.
05:25He will therefore accept the piece, and vote for Connie to get the other 99, leaving Donnie without money and in the minority.
05:34All right, now another step back.
05:37And we have Bernie, on stage as a proposer.
05:40Seizing all the money is still not an option.
05:43And now, there are three votes against him.
05:46But he has the decisive vote, so he only has to get a single vote again.
05:51This will make two votes for his share, two against, and his additional vote to cut the waste in his favor.
05:58The simplest way for Bernie to get the most pieces is to offer a piece to Donnie.
06:03It is because everyone knows that if Bernie leaves, Connie will end up with 99 pieces, Ernie with only one, and Donnie with empty pockets.
06:13So, the fortune favors Donnie, who gets a piece on this turn, and Bernie wins the lot by taking the rest.
06:20Sorry, Connie and Ernie, you get nothing this time.
06:25Finally, let's put Arnie back on the right track, and in charge of the voting process.
06:29So, he has four votes against him if he tries to seize it.
06:32One bought vote is not enough, since there will be three others left.
06:35This means that he needs at least two votes for his offer to work.
06:40Buying Bernie's vote makes no sense, because if Arnie leaves, Bernie will get 99 pieces.
06:46At the same time, Donnie will get a piece if Bernie wins.
06:50But Connie and Ernie, as we remember, will get nothing.
06:54This leaves Arnie with a simple choice.
06:57He can offer a piece to Connie, and another to Ernie to win their vote.
07:01And the final distribution is as follows.
07:0398 pieces for Arnie, none for Bernie, one for Connie, zero for Donnie, and one for Ernie.
07:09This will make three votes in favor of the distribution, and Arnie will win.
07:13The funny part of this situation is that the weakest pirates have the power to make the strongest escape, but they won't.
07:21They all know that they will end up with nothing if the distribution fails.
07:25So they accept very little.
07:27And as the rule of the majority applies, it is not even necessary to buy them all.
07:32Likewise, if there were ten pirates instead of five, the strongest would end up being the richest again.
07:38He would only have to offer a piece to each other pirate, leaving him only 96 pieces.
07:44However, he must be careful not to offer a piece to the one who is just after him.
07:49So it would be nothing for the second pirate, one for the third, none for the fourth, and so on.
07:55Now, you know how to share a treasure and always win, if you are strong enough, of course.
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