Please try it. At this time, you will find that you can achieve your goal by turning three somersaults. The explanation is as follows:
With+1, the cup mouth is up,-1, and the cup mouth is down. These three flipping processes can be simply expressed as follows:
Initial state:+1,+1,+1,+1.
First flip:-1,-1,-1,-1,+1.
Second flip:-1,+1,+1,+1,-1,+L.
The third flip:-1,-1,-1,-1.
If you change the 8 blocks in the question into 7 blocks, can you turn them all down several times (4 blocks at a time)?
After several experiments, you will find that you can't refuse them all.
Is it yours? Flip? Poor ability, or can't you finish it at all?
1? I'll tell you, no matter how many times you turn it over, you can't let these seven cups face down.
There is a simple reason. +1 means that the cup mouth is up,-1 means that the cup mouth is down, and the question becomes:? Change the symbols of 4 of 7+1 at a time, and whether they can all become-1 after several times. Considering the product of these seven numbers, because the sign of the four numbers changes every time, their product will never change (that is, it will always be+1), but in the case of all cups falling down, the product of seven numbers cannot be equal to-1.
The reason is so simple and the proof is so clever, thanks to 1? Language.
In China's chess, the horse goes to the sun. Did you find the following phenomena during the game?
When a horse jumps from a certain position, it must go through even steps to return to its original position.
There are nine chessboards? 10=90 positions, and adjacent positions are represented by numbers with different symbols (+and-1) (all solid point positions in the figure are represented by+1, and the rest are represented by-1), then the sign of the chess horse will change every step from any position. In other words, the chess horse will change its symbol.
Simple and beautiful mathematics tabloid content 2: the story of mathematician, the short story of mathematician Chen Jingrun.
Chen Jingrun, who lives in a six-square-meter cabin in 1966, borrowed a dim kerosene lamp and leaned against the bed board. He used a pen, consumed several sacks of draft paper, and actually conquered the world-famous math problem? Goldbach conjecture? In (1+2), the crown of number theory (1+ 1) is just one step away from picking up pearls. He proved it? Every big even number is the sum of the product of a prime number and no more than two prime numbers? , making him a world leader in Goldbach's conjecture research. This result is internationally recognized? Chen Theorem? , widely quoted. This work also enabled him, Wang Yuan and Pan Chengdong to win the first prize of China Natural Science Award with 1978 * *. His achievements in studying Goldbach conjecture and other number theory problems are still far ahead in the world. World-class master of mathematics, American scholar? Will (a? Weil) once praised him: Every job in Chen Jingrun is like walking on the top of the Himalayas.