It is said that at a cocktail party, many mathematicians got together, talking and laughing, filled with a relaxed and happy atmosphere. Feng, a famous master of mathematics and the "father of electronic computers"? Neumann raised his glass and talked and laughed with his colleagues. Have any guests seen Feng? Neumann sometimes appears absent-minded and thoughtful. He knows that this is an "occupational disease" for scientists: he is used to scientific research and thinking about "gymnastics", and if he doesn't want to ask questions, he seems to have lost something. So he asked a question.

"Hey, feng? Neumann successively, want to play games? "

"the game." Pointing to his head, he said, "It is trying to move around and become a thinking game!" "

"I have a bee problem here. The distance between the two trains is 100 miles. They are running in opposite directions on the same track, and the speed is 50 miles per hour. There is 1 bee at the front end of train A flying to train B at the speed of 100 miles per hour. After meeting with the B train, they immediately turned back and flew to the A train at the same speed. After meeting the A train, they turn back and fly to the B train at the same speed, and so on until the two trains meet. Assuming that the time for a bee to make a circle is negligible, then this bee (Feng? Neumann interjected: What a super bee! ) How many miles did a * * * fly? "

Feng? Neumann, the most outstanding mathematician in the 20th century, has strong mental arithmetic ability, and can calculate skillfully without paper and pencil. It is said that he could mentally calculate the division of eight figures at the age of six, mastered calculus at the age of ten, and ranked first in the Hungarian mathematics competition in middle school. His teacher, famous mathematician and educator Paulia recalled: "John (Feng? Neumann's name is the only student I am afraid of. If I list a problem in my speech, then at the end of the speech, he will always take a scribbled piece of paper and say that he has solved it. "

At this time to solve interesting math problems as an active rest, to participate in a game, Feng? Neumann did not use simple arithmetic methods, but skillfully adopted ingenious solutions in advanced mathematics, which quickly solved the problem.

If it is solved directly from the round-trip flight distance of bees, it will be very complicated; It is very simple to solve indirectly through the flight time of bees.

Because the two trains are 65,438+000 miles apart and moving towards each other at a speed of 50 miles per hour, the time that passed when they met was 65,438+0 hours. During this time, bees kept flying back and forth in front of the two trains, and the whole time of bees flying happened to be the time when the two trains met. So, the bees flew 1 hour 100 mile.

Interestingly, Professor Su, a famous mathematician in China, blurted out a "hunting dog problem" similar to the "bee problem" put forward by foreign mathematicians when visiting abroad. Hunter A took his hounds to Hunter B's house, which is120km away. When A set out, B just went out to meet A .. A walked 10 kilometers per hour, B walked 20 kilometers per hour, and the hound walked 30 kilometers per hour. The hound first met B, then returned to meet A, then turned to meet B. So the hound ran back and forth between A and B. Q: How many kilometers did the hound run when A and B met?

Because the whole time of the hound running back and forth happens to be the time when hunters A and B meet, 120 ÷ (10+20) = 4 (hours).

So, the distance that hounds run is * * *

30× 4 = 120 (km).