1. The length of a rectangle is twice its width. If the length is increased by 5cm and the width is decreased by 3cm, the area of the new rectangle is more than the original one18cm2. Find the length and width of the original rectangle.

There are three people to take part in the competition. They choose a door from three doors: A, B and C respectively. After the game, the host asked the first person, "What is behind the door you chose?" The first man said, "I chose door A." The host asked the second person, "What is behind the door you chose?" The second man said, "I chose the second door." The host asked the third person, "What is behind the door you chose?" The third man said, "I chose door C." The master opened the door and found a goat inside. Excuse me, what is behind the door chosen by the second person?

Four people want to cross the bridge. They only have one flashlight. A flashlight can only illuminate the person in front, but not the person behind. Every time you cross the bridge, you have to shine a flashlight on two people to cross it. The crossing time for each person is 1 minute, 2 minutes, 5 minutes and 10 minutes respectively. When two people cross the bridge together, their speed is determined by the slower one. Ask them how long it will take at least to cross the bridge.

There is a square pond surrounded by trees. The distance between each tree is equal. Now we should plant a new tree in the pond, so that the distance between the new tree and each tree is equal. Excuse me, where should the new tree be planted?

These interesting math problems can help junior high school students exercise their logical thinking ability, spatial imagination and mathematical reasoning ability. At the same time, they can also make learning mathematics more interesting and meaningful.