(1) proves that algebraic expressions are even numbers.
(2) Find the maximum value that this algebraic expression can take.
2. Fill 1.2.3, …, 9 into nine small circles of a big circle (that is, nine points on the side of the big circle) at will, and prove that the sum of the numbers of the three small circles must be greater than 15.
3. There are 17 teacups on the table, all with their bottoms facing up. Turn six cups at a time. After several turns like this, can the cups of this 17 teacup all face up? Why?
Answer: 1. In the algebraic formula ruz-zwy-suz+swx+tuy-tux, r, s, t, u, v, w, x, y and z can be+1 and-1 respectively.
(1) proves that algebraic expressions are even numbers.
(2) Find the maximum value that this algebraic expression can take.
( 1)ruz-zwy-suz+swx+tuy-tux
The solution is wrong, because r = 1 and-1, and the positive and negative results are different when other values are unchanged.
The method is to see whether only odd terms in the formula change when a variable changes positively or negatively, so the parity remains unchanged.
(2) Because the first question is wrong, the second question cannot be solved.
But I can tell you what to do!
You can take any item and make the result 1, so there are four collocations of three variables, 1 1, 1- 1,-1.
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2. Fill 1.2.3, …, 9 into nine small circles of a big circle (that is, nine points on the side of the big circle) at will, and prove that the sum of the numbers of the three small circles must be greater than 15.
There is something wrong with the topic, because it should be said that the sum of three consecutive small circles must be greater than 15.
1+2+...+9 = ( 1+9)9/2 = 45
45*3/9 = 15
It can be seen that the average value of the sum of three numbers is 15.
therefore
(1) If the sum of three numbers is less than 15, then the sum of three numbers must be greater than 15.
(2) Are they all equal to 15? Don't! Because they are nine different numbers.
So the proposition is proved!
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3. There are 17 teacups on the table, all with their bottoms facing up. Turn six cups at a time. After several turns like this, can the cups of this 17 teacup all face up? Why?
It should be all up, and all down after the reaction! Or face down, face up after turning around, please pay attention in the future! ! !
Solution:
Sure!
( 17+ 1)/6 = 3
Then in order to realize the meaning of the problem, a cup must be turned over at least three times, otherwise it will be reversed.
123456 turn once.
6789, 10, 1 1, 12 turn once.
6, 13, 14, 15, 16, 17 turn once.
Among them, 6 cases turned over 3 times.