A decision question

The title is as follows: card chip champions Joe, Gordon, and Susan have a hotel, "Mr. They need $25,000 to pay off their debt, but they do not get bank loans because of poor credit. They had to turn to their competitors, hoping to sell their hotels to their competitors cheaply. However, their competitors felt that they had a full chance to get the hotel's Grand Prix, so they proposed the following suggestions:

"I have five chips in my pocket-three black chips and two white chips. I suggest you put your eyes on it and give each of you a chip. You will be allowed to watch the chips in your companions, but you must hide your chips in your hands. If either of you can tell me the color of your chips, I will give you $1 million. In addition to coping with your current financial difficulties, you can also ensure that your future financial problems are resolved. Each of you can choose to guess or not guess. However, if any of you guessed it wrong, you would have to pay your hotel to us for free. Is this a good deal ?"

These partners have no choice but to have other hopes, so they have accepted the challenge. So the competitor showed them five chips-three black chips and two white chips-and when they covered their eyes, they gave each one a chip, then I put two useless chips back in my pocket.

Joe's blind eye was uncovered. He looked at the chips of his companions, but although he tried his best to use logical thinking, he could not determine the color of his chips. He chose to give up and leave the opportunity to the other two companions. Gordon's blindfold was uncovered. After seeing the chips of his companions, he could not guess the color of his chips. He gave Susan the opportunity.

The competitor smiled. When he began to move Susan's blindfold, he didn't give her any more opportunities than Joe or Gordon. However, Susan cut him off with confidence. "You can mask my eyes. There is no difference between it and it. I will get that $1 million! I learned from my peer's answer that my chips are --." She was right. This victory saved the hotel's security.

How does Susan know the color of his chips?

 

My derivation is as follows: After competitors give each of them a single chip, the remaining chips in their hands may only be 2 white, 2 black or 1 black and 1 white. The three cases are listed as follows:

1) if the competitor has two white chips:
Joe will see that the other two are black chips, and they will hold black chips;
Gordon will see that the other two are black chips, and they will hold black chips;
Susan holds black chips.

2) If the competitor has two black chips:
Joe may encounter two situations:
① The other two held white chips. At this time, he could export his hands and he must hold black chips. It is inconsistent with the question settings, so this situation will not occur;
② The other two held a black chip and a white chip respectively.
Similarly, like Joe, Gordon has two situations:
① The other two held white chips. At this time, he could export his hands and he must hold black chips. It is inconsistent with the question settings, so this situation will not occur;
② The other two held a black chip and a white chip respectively.
Susan may hold black chips or white chips.

3) if a competitor holds 1 black, 1 white, and 2 chips:
Joe may encounter two situations:
① The other two held black chips, and now they held white chips;
② The other two held a black chip and a black chip respectively.
Similarly, like Joe, Gordon has two situations:
① The other two held black chips, and now they held white chips;
② The other two held a black chip and a black chip respectively.
Susan may hold black chips or white chips.

There are too many situations for Joe and Gordon. We can't push them down. We can start with Susan in another direction. Susan's chips are not black or white.
① Suppose Susan's chips are white. At this time, Joe should see the other two holding 1 black 1 white (2 white was denied), he could not guess the color of his chips, because he may hold black or white. Gordon sees that the other two hold 1 black and 1 white respectively, and then he will make the following derivation: competitors in order to win, so that one of the three won't be able to determine the color of their chips after seeing the chips of the other two, and he won't be able to leave two black chips. From this, we can conclude that Joe holds black chips, Susan holds white chips, and Susan holds black chips. However, Gordon cannot export the color of his chips. Susan won't hold white chips.
② Let's look at the assumption that Susan's chips are black. At this time, Joe either sees the other two holding 2 black, or the other two holding 1 black and 1 white, he may hold black or white. Like Joe, Gordon either saw the other two holding 2 black, or saw the other two holding 1 black and 1 white, he may be holding black or white. However, no matter what Gordon and Joe will see, Susan must be black. This is exactly the same as the question that Susan does not see. Bingo !!!

The final answer is: Susan holds a black chip.