Math Problem A hundred pirates come to an island and find 100 gold bricks, how do you divide them?

To solve this kind of problem, we always push backwards from the last situation so that we know what is good and bad to decide in the last step. And then using this knowledge, we can get the final second step to decide what to do, and so on. If we start with the problem, it's easy to get stuck in the way

If I had made such a decision, what would the next pirate do? ”

With this in mind, consider the situation where there are only 2 pirates (all the other pirates have already been thrown into the sea to feed the fish). They are called P1 and P2, with P2 being the more ferocious. The best solution for P2 is, of course:

He gets 100 gold coins for himself, and 0 for p1. When voting, his own vote is enough for 50%.

Take it a step forward. Now add a more ferocious pirate who knows - P3 knows he knows - if P3's plan is rejected, the game will continue only with P1 and P2, and P1 will not get a single gold coin. So P3 knows that as long as P1 is given a little sweetness, P1 will agree to his plan (of course, if P1 is not given a little sweetness, he won't get anything anyway, P1 would rather vote for P3 to feed the fish).

So the best solution for P3 is: P1 gets 1 piece, P2 gets nothing, P3 gets 99 pieces.

The situation is similar for p4. All he needs to do is get two votes, and giving P2 a gold coin will make him vote for the plan, because P2 won't get anything in the next P3 plan. P5 also had the same reasoning method, except that he had to convince his two companions, so he gave each of P1 and P3 who got nothing in the P4 scheme a gold coin, leaving himself 98 coins.

And so on, the best option for the P100 (the eldest of the 100 pirates) is to get 51 for himself, giving each of the P2, P4, P6, and P8 ...... that gets nothing in the P99 planp98 a gold coin.

You said that the boss ended up with 50 pieces, maybe he counted himself when he counted all the even numbers?

The main idea of this question is that, contrary to what many people think, half of the people in any distribution plan will get nothing. Because the allocator only needs to get half of the votes. Those who don't need it don't have to bother.

Then the previous allocator only needs to "buy" these people with 1 gold brick per person. You can get all the remaining gold bricks.

It should be half of the second child's half, and half of his own.

The boss said, "You divide the rest, give me the rest, and if you can't leave it, you don't want it, but it must be divided equally."

Throw all the 98 pirates below the third child into the sea, and then only the eldest and second are left with 50 yuan.

One for each person.

Who will still be the sea? Gold? Pirate?

Five pirates have grabbed 100 gems, each of the same size and price.

They decided to divide it like this:

1。Draw lots to determine your own numbers (1, 2, 3, 4, 5).

2。First of all, the 1st proposes a distribution plan, and then the 5 people vote, and when more than half of the people agree (including half), they will be distributed according to his proposal, otherwise they will be thrown into the sea to feed the sharks.

3。If No. 1 dies, No. 2 proposes a distribution plan, and then the four of us vote, and if and only if more than half of the people agree, the distribution will be made according to his proposal, otherwise they will be thrown into the sea to feed the sharks.

4。And so on.

ConditionsEvery pirate is a very smart person, and can judge the gains and losses very rationally, so as to make a choice.

Question 1: What kind of distribution plan does the pirate propose to maximize his profits?

It would be even better if the following clause were added to the rule: pirates would be happy to see other pirates thrown into the sea to feed sharks while maximizing their own profits. Without mentioning the past, it is in the best interest of each pirate that other pirates are thrown into the sea to feed the sharks. ）

Reasoning process. Inference :

Suppose the number has been thrown into the sea, and the jewel is divided by the number 4.

Reasoning from hypotheses:

Conclusion: The plan of No. 4 must be , and it must be passed. (Therefore, No. 4 could not have been thrown into the sea, which does not contradict the hypothesis).

Reasoning :(to use the conclusion of reasoning).

Suppose the number has been thrown into the sea, and the number 3 is divided into gems.

Reasoning from conclusions and assumptions:

Conclusion: No. 3 conducts "reasoning" reasoning, and after getting the conclusion, he knows: he only needs to give No. 5 more than 0 gems, that is, the plan is , and the plan will definitely pass.

Therefore, No. 3 cannot be thrown into the sea, and it does not contradict the hypothesis, as long as it does not contradict the hypothesis, and has nothing to do with the hypothesis, because they are two independent inferences. ）

The rest of the reasoning is so on.

The final result was 96