Logic Analysis and reasoning (Piracy and gold issue)

Original question:

Five pirates, divided into 100 gold. They put forward a scheme in sequence. If half or more of them agree to the scheme, they will pass the scheme, but they will throw the proposed solution to the sea, continue to split the gold.

If a pirate wants to survive and maximize the benefits, how can the first pirate propose a gold splitting solution?

 

The analysis process is as follows:

If he wants to get all his gold from the first pirate, then other pirates will not agree, and he will surely be in the sea to survive, he must give some gold to other pirates. How can he score?

This is the key. In fact, a very important point is to consider the idea of every pirate, that is, how much gold they need to obtain before they can support the first pirate.

Therefore, the analysis here should begin with the last pirate idea.

 

Assume that five pirates are A, B, C, D, and E.

As the last pirate E, he certainly hopes that all the previous pirates will die, so that he can take all the gold, but this is impossible, at least the pirate D in front of him must have taken all the gold before him.

If only D and E are left, D will take all the gold as his own, because even if no gold is given to E, his vote rate is also 50%, e won't let the C pirate die. (In this way, there will be C, D, and E ),

C. In order to get the pass rate, it will certainly be divided into some E (of course, C can also be considered to be allocated to D, but how much is assigned to D? In addition, C wants to maximize its own interests, and d always wants C to die, so C will not be distributed to D ).

Similarly, if only C, D, and E are left, D will certainly not agree with C's proposal. Because d wants C to die, C only needs to give e a gold, e can support C, thus reaching a support rate of more than 50%,

In this way, d won't get any gold, so D will consider that it won't want C's superior B to die, otherwise he will have no gold.

In this way, the Four pirates B, C, D, and E divide gold. C will certainly not agree with B's proposal, because C wants B to die. So, to get a 50% support rating, B should win at least one person. This person is d,
Because d does not want B to die, B's allocation scheme will be: 99: 0: 1: 0. But B cannot give E, because even if B dies, e can get a gold,

To get the support of E, we need to give e two gold, and B's benefits will be reduced.

Now let's consider the situation where A, B, C, D, and E are gold. To survive, A must be supported by at least two other pirates, B is not considered, because B is bound to expect a to die, so that B can get the most gold.

C is easy to buy, because C didn't get gold in the last round of analysis, so just give him a gold. For D and E, buying e is easier, because he didn't get gold in the last round of analysis,

And he is a pirate related to the interests of C, so he is the best choice to preserve a and get at least one gold. Therefore, the final result is: 98: 0: 1: 0: 1.

 

Through the above analysis, we can see such an analysis process for such a type of questions.

Here is a reference answer to the question:

① If only the solutions for D and E piracy are left: 100: 0

② If only the solutions for C, D, and E are left: 99: 0: 1

③ If only the solutions for B, C, D, and E are left: 99: 0: 1: 0

④ If it is proposed by pirate A, the solution is: 98: 0: 1: 0: 1.

 

The answer is complete.

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