No.11 (Separating socks for the blind)

Put them in the sun.

After a period of time

The black socks have a significantly higher temperature, and the white socks have a lower temperature. Each person gets two pairs of hot ones and two pairs of cool ones.

No.12 (The King and the Prophet)

This is a logical paradox. The correct answer is: He predicted that he would be beheaded. If he is hanged, it means that his words are correct, but not consistent with the facts; if he is beheaded, it means that the prediction is wrong, but in fact it is correct. Because the king believes that the prophet's answer is correct, then according to his prior promise, he should Let the prophet take poison and die, but this is not consistent with the answer of hanging the prophet, so he cannot execute the prophet

No.13 (Weighing the ball problem)

Points Three groups: four in each group, the first group is numbered 1-4, the second group is 5-8, the third group is 9-12.

First weighing: Place the first group on the left side of the scale, and the first group on the right side. Put the second group.

A The first possibility: balance. The difference is in the third group.

Next, you can place numbers 9, 10, and 11 on the left, and the three normal numbers 1, 2, and 3 on the right.

a. If it is balanced, then No. 12 is different;

b. If the left is heavy and the right is light, then No. 9, 10, and 11 are different, and they are smaller than normal balls. Heavy. Weigh again: 9 is placed on the left and 10 is placed on the right. If it is balanced, then No. 11 is different; if the left is heavy and the right is light, then No. 9 is different; if the right is heavy and the left is light, then No. 10 is different.

c. If the left is light and the right is heavy, the reason is the same as b

B The second possibility: the left is heavy and the right is light, then the difference is in numbers 1-8, but I don’t know if it is more normal Is it light or heavy?

The second weighing: place numbers 1, 2, and 5 on the left, and numbers 6, 9, and 3 on the right.

a. If balanced. The difference is in 4, 7, and 8. You can weigh it for the third time: put 4 and 7 on the left and 9 and 10 on the right. If it is balanced, then 8 is different; if the left is heavy and the right is light, then 4 is different; if the left is light and the right is heavy, then 7 is different.

b. Still heavy on the left and light on the right. The difference is in 1, 2, and 6 whose positions have not changed. You can weigh it for the third time: put 1 and 6 on the left and 9 and 10 on the right. If it is balanced, then 2 is different; if the left is heavy and the right is light, then 1 is different; if the left is light and the right is heavy, then 6 is different.

c: Left light and right heavy. The difference is in 5, 3, and 5, because only they have changed their original positions. You can call it the third time: put 5, 3 on the left, 9, 10 on the right. If the left is light and the right is heavy, then 5 is different; if the left is heavy and the right is light, then 3 is different.

C The third possibility: left is lighter and right is heavier, the same reason as B

At this point, no matter what happens, you can find the difference by weighing it three times, and you know it is lighter than normal. Still heavier.

No.14 (three light bulbs)

First switch on the switch in that room and turn on a light. Wait 5-10 minutes to close it and then open another one.

Then go to the light room. One bulb is hot, one is bright, and one is out.

No.15 (Black Hat Dance)

It doesn’t matter if there are 50 or 200 people. The key is that the answer to this question is fixed at 3 black hats.

In addition, the way of thinking about this answer is wrong. How can we just assume that three people wear three black hats?

I think it should be that if there is only one black hat, the first time the person wearing the black hat sees everyone wearing white will immediately burst into applause. So the result for the first time is that people know that there are at least 2 black hats, and at least 1 black hat has been seen. The second time, there was still no applause. If there are only 2 black hats, then these two people should definitely burst into applause when the lights are turned on this time, indicating that there are at least 3 black hats. And so on.