1. If it takes one hour to burn an uneven rope, then how to use it to decide half an hour?

It takes one hour in all to burn an uneven rope from beginning to end. Now there are several ropes of the same material, then how to use the method of burning ropes to time one hour and fifteen minutes?

2. One hit-and-run accident occurred in one city. There are only cars of two colors in this city: blue (15%) and green (85%). When it happened, one person saw the car on the spot; he testified that it was a blue car. But according to the experts’ analysis on site, the accurate possibility in that condition at that time is 80%, then, how much is the probability that the accident car is a blue car?

3. One paid 8 yuan for a chicken and sold it for 9 yuan. He felt it was not worthy, then bought it back for 10 yuan and sold for 11 yuan to another person, then how much he made?

4. There are three buckets, the two bigger ones can hold 4 kilos of water respectively, the smaller one 3 kilos. Now the two bigger ones are full and the smaller one is empty, how to distribute the 8 kilos of water to four people, each one with 2 kilos. (There are no any other tools and four people with their own containers. The distributed water can not be gotten back. )

5. Xiao Ming and Xing Qiang are Mr Zhang’s students. Mr Zhang’s birthday is M the Nth. They both know his birthday is one of the following ten dates. Mr Zhang told M to Xiao Ming and N to Xiao Ming. Mr Zhang asked them if they knew his birthday. The ten dates are March 4th, March 5th, March 8th, June 4th, June 7th, September 1st, September 5th, December 1st, December 2nd and December 8th.

Xiao Ming said: If I don’t know it, neither does Xing Qiang definitely.

Xiao Qiang said: I couldn’t have known it, but I know it now.

Xiao Ming said: Oh, then I know it, too.

Please decide Mr Zhang’s birthday according to the above dialogue.

6. There are two blind people and they bought two black pairs of socks and two white pairs of socks respectively. The eight pairs of socks are of the same cloth material and size. But every pair of socks is attached to a tag. They carelessly mixed the eight pairs of socks. How can they get back their own two black and two white pairs of socks respectively?

7. Known conditions: every plane has only one tank, planes can fill the tanks one another (They fill the tanks one another and there isn’t any filler.) One tank of oil can provide one plane to fly around the earth for half a circle.

The question: In order to let at least one plane to move a circle around the earth and return to the take-off airport, how many planes are needed at least to start off? (All planes take off from the same airport and must return to the airport safely. They can’t land off midways and there isn’t any airport.)