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

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

Use A1, A2, A3, A4 for the larger number in each group A 50 means
For the smaller number, use B1, B2 B50 means
（|a-b|+a+b）= （a-b+a+b）
The sum of these 50 values is
（a1-b1+a1+b1+a2-b2+a2+b2… +a50-b50+a50+b50）
= （a1+a2+a3+… +a50-b1-b2-… -b50+a1+b1+a2+b2+… +a50+b50）
= （a1+a2+a3+… +a50-b1-b2-… -b50+1+2+… +100）；
（a1+a2+a3+… +a50-b1-b2-… -B50) maximum
Obviously (51 + 52 +) +100-1-2-… -50）；
The maximum of the sum of these 50 values
（51+52+… +100-1-2-… -50+1+2+… +100）
= 2×（5050-1275）
=3775．
So the maximum value is 3775