Four-color theorem

1. Angle trisection problem: divide any given angle into three equal parts.

2. Cubic product problem: Find the side length of a cube so that the volume of the cube is twice that of the known cube.

3. Turn a circle into a square: find a square and make its area equal to that of a known circle.

Fermat's last theorem

A pirate robbed 100 jewels, each of which was the same size and priceless. They decided to divide it like this:

1, draw lots to decide your own number (1, 2, 3, 4, 5)

2. First, 1 put forward the distribution plan, and then five people voted. When and only when more than half of the people agree, they will be distributed according to his proposal, otherwise they will be thrown into the sea to feed sharks.

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

4, and so on

Conditions:

Every pirate is a very smart person, who can rationally judge gains and losses and make choices.

Question:

What is the final distribution result?

Tip:

The judgment principle of pirates:

1, help

2. Get as many gems as possible

3. Kill as many people as possible

1) Change the rules, the scheme must get more than 50% of the votes in the voting (the proposer who only gets 50% of the votes will also be thrown into the sea to feed the fish), so how to solve the problem of 10 pirate points 100 gold coins?

2) Without changing the rules, what will happen if 500 pirates share 100 gold coins?

3) If each pirate has 1 gold coin in his savings, he can use this gold coin in the distribution scheme. If you throw him into the sea to feed the fish, his savings will be merged into gold coins for distribution. What about this time?

I hope you can talk more about some difficult problems in world mathematics and be more detailed. The more, the better. I have better answers, and some of them already have answers.