Put 1, 2, 3 The 100 natural numbers are randomly divided into 50 groups with two numbers in each group. Now, mark any number in each group as a and the other as B, and substitute them into the algebraic formula 0.5 (| A-B | + A + b) to calculate the result. After 50 groups of numbers are substituted, 50 values can be obtained, and the maximum sum of these 50 values can be obtained
max(a,b)=0.5(|a—b|+a+b)
So the maximum value of the sum of 50 values should be: 51 + 52 + 53 +. + 100 = (51 + 100) * 50 / 2 = 3775
RELATED INFORMATIONS
- 1. Divide the 100 natural numbers 1,2,3,4 ······ 100 into 50 groups with two numbers in each group. First, record any number of the two numbers in each group as a The other is denoted as B, which is substituted into the algebraic formula 1 / 2 (| a + B | + A + b) to calculate the result. After 50 groups are substituted, 50 results can be obtained, and the maximum value of these 50 values can be obtained
- 2. The 100 natural numbers 1,2,3, ·······, 100 are randomly divided into 50 groups, each group has two numbers, one of which is recorded as a, the other as B, Substituting into the algebraic formula # (189); (a + b-la-bl), we can get the result. After 50 groups are substituted, we can get 50 values, and find the minimum value of the sum of these 50 values (briefly explain the reason)
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- 4. Put 1,2,3 The 100 natural numbers are randomly divided into 50 groups with two numbers in each group. Now, one of the two numbers in each group is recorded as a and the other as B
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- 9. Mathematical problems are expressed in algebra Fold a piece of paper in half once to get a crease, the second time to continue to fold to get three creases, the third time to fold to get seven creases, then the total number of creases is ()
- 10. A mathematical problem of algebra If the nonzero real numbers a and B satisfy a ^ 2 + A-1 = 0 and B ^ 2 + B-1 = 0, then the value of B / A + A / B is?
- 11. Put 1,2,3 The 100 natural numbers are randomly divided into 50 groups with two numbers in each group. Now, one of the two numbers in each group is recorded as a and the other as B Take it into algebraic formula 1 / 2 (a + B - | A-B |) to calculate and get the result. After 50 groups are brought in, you can get 50 values, and find the [minimum value] of the sum of these 50 values
- 12. Put 1, 2, 3 These 100 natural numbers are randomly divided into 50 groups with two numbers in each group. Now, any one of the two numbers in each group is recorded as a and the other as B , which can be substituted into the algebraic formula 1 / 2 (| A-B | + A + b) for calculation, and the results can be obtained. After 50 groups of substitution, 50 values can be obtained, and the maximum value of sum can be obtained
- 13. If a natural number (except 0) is an odd number multiplied by 3 plus 1, and an even number divided by 2, what will happen? What is this phenomenon called? Why
- 14. For a natural number, do the following operation: if it is an even number, divide by 2; if it is an odd number, do the following operation for a natural number: if it is an even number, divide by 2; if it is an odd number, add 1. Do this until 1, and the operation stops. Find how many numbers become 1 after 10 operations?
- 15. If it is even, divide it by 2. If it is odd, multiply it by 3 and then add 1, What's the final result, A0, B1, C2, D3
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- 17. The difference between a natural number and its reciprocal is 32 / 33. What is it
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