Puzzle guessing hat trick watching face slap activity

A group of people held a dance party, and everyone had a hat on their head. There are two kinds of hats, black and white, at least one black. Everyone can see the color of other people's hats, but not their own. The host first asked everyone to see what hats others were wearing, and then turned off the lights. If someone thought they were wearing black hats, they would slap themselves in the face. Turning off the lights for the first time, no sound. So I was turning on the lights, watching, and everyone was still silent after watching. It wasn't until the third time that the lights were turned off before there was a crackling slap in the face. Ask how many people wear black hats

Thinking analysis

Suppose you are wearing black hats and gradually increase the number of people wearing black hats.

Suppose there is only one person wearing a black hat

If you are the only person wearing a black hat, then I found out on the first night because there is at least one black hat, so the number of black hats is greater than 1.

Assume that two people are wearing black hats and assume that they are wearing a hat

We divide the time into light on time 1 light off 1 light on time 2 light off 2 light on time 3 light off 3

1. Turning on time 1 When turning on the lights, I can only see one with a black hat B and a group of white hats
2. Turn off the lights 1 When turning off the lights, I saw that B didn’t slap himself, so I suspected that he found that I was also a black hat, so he didn’t slap himself.
3. Lights on time 2 I can still only see black hats B when the lights are turned on, but I know in my heart that I must also be black hats, otherwise B will definitely beat himself
4. Turn off the lights 2 Turn off the lights. I already know that I have a black hat, so I hit myself B. I also know when I see it. So turn off the lights 2. There will definitely be a slap in the face.

Assume that all three people are wearing black hats. Assume that they are wearing a hat.

We divide the time into light on time 1 light off 1 light on time 2 light off 2 light on time 3 light off 3

1. Lights on time 1 Lights on time I saw two black hats BC and white hats
2. Turn off the lights 1 Turn off the lights when I saw BC did not slap in the face, I guess B suspected CC suspected B
3. Turning on time 2 When turning on the lights, I saw two black hats BC. If BC slapped my face tonight, there are the above assumptions, then I am definitely not a black hat.
4. Turn off the lights 2 Turn off the lights and the time is still silent
5. Lights on time 3 Lights on time Turns off time 2 No one slapped the light so there must be more than 2 people with black hats, but I saw 2 at the light-on time, so I concluded that I must be wearing a black hat
6. Turn off the lights 3 I came to the conclusion that I was wearing a black hat, I slapped myself first and then crackled

**Then some friends have to ask why it can’t be four or five.** The reason is as follows. I only learned that the number of people was greater than 2 before the third turn-off time, but what I saw was 2 people at the turn-on time. If I When I turned on the light and saw 3 people or more, then the third time I turned off the light, I couldn’t conclude that I was a black hat, and there would be no slap in the face.