Can $Ana$ complete the second row so that $Beto$ does not achieve his goal?
Source: May Olimpiad 2019 Level 1 P5
March 9, 2021
combinatorics
Problem Statement
There is a board with three rows and columns. In the first row are written the numbers integers from to inclusive, ordered from smallest to largest. In the second row, writes those same numbers but ordered at your choice. In each box in the third row write the difference between the two numbers already written in the same column (the largest minus the smallest). have to paint some numbers in the third row so that the sum of the numbers painted is equal to the sum of the numbers in that row that were left unpainted. Can complete the second row so that does not achieve his goal?