Chapter 1: Find the perimeter of acute triangle by clever thinking.
Math brain teaser: The lengths of three sides of an acute triangle are both double digits, and they are three consecutive even numbers. The sum of their numbers is a multiple of 7. What is the longest circumference of this triangle?
Answer: The three sides of a triangle are three consecutive even numbers, so their unit digits can only be 0, 2, 4, 6, 8, and their sum is an even number. Their sum of unit digits can only be a multiple of 7 and can only be 14. The three sides of a triangle may be 86, 88 and 90, and the longest circumference is 86+88+90=264.
Article 2: Adults and children eat 100 steamed bread separately.
Math brain teaser: 100 steamed stuffed bun, 100 people to eat, 1 adults to eat three, three children to eat 1. How many adults and children can eat it?
Answer: 25 adults and 75 children.
Part III: Steps
Math brain teaser: both the office building where Xiaoming works and the family building where he lives are 6 floors, while the floor where Xiaoming works and lives is 3 floors. How many steps does Xiao Ming climb every day compared with his colleagues who live and work on the sixth floor?
Answer: If you don't think about it, it's easy to draw half a conclusion, but this conclusion is wrong. The key here is that people who live on the first floor don't need to climb stairs. If you want to go to the third floor, you need to climb two steps instead of three. If you want to go to the sixth floor, you need to climb five steps instead of six. The answer is two fifths.
Chapter four: the ingenious allocation of rooms by tour groups
Math brain teaser: There is a tour group of 80 people, including 50 men and 30 women. There are three types of rooms in their hotel: 1 1, 7 or 5 people. Men and women live in different rooms. How many rooms do they need?
Answer: In order to minimize the number of rooms, first try to arrange rooms for 1 1 person, so that 50 men will arrange 1 1 three rooms, five two rooms and seven rooms 1 room. 30 women should be assigned to11room, two 7 rooms, 1 5 room, and * * * has 10 room.
Chapter 5: Weighing out unqualified parts with scales.
Math brain teaser: There are 13 parts with the same appearance, but one part is unqualified, its weight is different from others, and its weight is unknown. Please weigh it three times and find out the answer.
Answer: First, put four parts on each side of the balance. If the balance is balanced, it means that the defective parts are in the other five, and it is not difficult to find them after weighing twice. If it is not balanced, it means that the bad ones are in eight. At this time, remember what is light and what is heavy. The remaining five are qualified and can be used as standards. Then put five qualified ones on the left side of the balance, and take two light ones and three heavy ones on the right. At this time, if the right end is low, it means that the bad one is in the triple and can be weighed out at one time.