The topic is as follows: Question 1: The last digit of a number is 40, and the first digit is 13. What's this number? The second question: add a stroke to the word "only" to make it another Chinese character. The third question: add a stroke to the word "person" to make it another Chinese character. (Except one, big) Question 4: Under what circumstances 0>2>5>0. Question 5: 62-63 = 1 Move only one number to make the equation hold (the symbol cannot move). Question 6: 5+5 = 550 plus a sum makes the equation hold (not an inequality). Question 7: There are two incense sticks with uneven distribution, and the burning time of each incense stick is one hour. What method can you use to determine the cross section? Question 8: You have four jars containing pills, and each pill has a certain weight. The contaminated pill is the uncontaminated weight+1. You only weigh it once. How do you know which jar is polluted? Question 9: Imagine you are in front of a mirror. Excuse me, why can the image in the mirror be upside down, but not upside down? Question 10: 1 yuan for a bottle of soda. After drinking, I will exchange two empty bottles for a soda. Q: If you have 20 yuan money, how many bottles of soda can you drink at most? Question 1 1: A group of people have a party, each wearing a hat. There are only two kinds of hats, black and white, and there is at least one kind of black. Everyone can see the color of other people's hats, but not their own. The host first shows you what hats others are wearing, and then turns off the lights. If someone thinks he is wearing a black hat, he will slap himself in the face. The first time I turned off the lights, there was no sound. So I turned on the light again and everyone watched it again. When I turned off the light, it was still silent. I didn't get a slap in the face until I turned off the light for the third time. How many people are wearing black hats? 1，432，300，000，000，000，000，000，000，000，000，000，000。 When guessing boxing, 5 moves the 6 of 62 to the upper right corner of 2, that is, the 6 th power of 2 is 2 6-63 = 1 6.5+5 = 550+. 8. Number the cans as 1, 2, 3, 4, 5, then take out 1, 2, 3, 4, 5 balls from each can and weigh them, and then-(1+2+3+4+5) the weighing result is No.9 of the contaminated can. 2) The symmetry between "mirror image" itself and the left and right "mirror image" of human body structure is the key to understand this problem. The "mixing" (confusion) and "sublimation" (illusion) of the two images lead to the conclusion that "images can be turned upside down, but not upside down". Analysis; Principle of flat mirror imaging! Draw a picture and you will understand! When you stand in front of a flat mirror, you will see that your image in the mirror is left and right opposite! In fact, up and down can also be reversed! Put the flat mirror on the ground. If you stand on a flat mirror, you will find that yours is upside down! Just like the reflection in the water you see by the lake! Buy 20 bottles of soda 10.40 bottles or 39 bottles to get 20 bottles. Now * * there are 20 bottles and then 10 bottles get 10 bottles. Now * * there are 10 bottles, and then 5 bottles get 5 bottles. Now * * * there are three bottles replaced by 1 bottle of soda 1 bottle, and now * * * there are two bottles replaced by 1 bottle, and now * * * there is 1 bottle borrowed from a passerby. I returned the bottle to passerby A * * and drank 20+10+5+2+1+1= 40 bottles of soda. If I don't touch passerby A, I have to drink 39 bottles. If you have two black hats, you will bump into yourself when you turn off the light for the second time, because he sees that others only have one black hat. But according to the above inference, if you only have a black hat, you will hit yourself the first time, so you are also a black hat. If you have three black hats, you will hit yourself when you turn off the lights for the third time. The same reason is the same as above. If there are n black hats, then turning off the lights for the nth time will hit you, mathematical induction