MathDB
Minimize the sum of difference squares

Source: KJMO 2018 p6

July 26, 2019
algebra

Problem Statement

Let there be a figure with 99 disks and 1111 edges, as shown below.
We will write a real number in each and every disk. Then, for each edge, we will write the square of the difference between the two real numbers written in the two disks that the edge connects. We must write 00 in disk AA, and 11 in disk II. Find the minimum sum of all real numbers written in 1111 edges.