min sum of 2-products in top row May Olympiad (Olimpiada de Mayo) 2019 L2 P2
Source:
September 24, 2021
combinatorics
Problem Statement
There is a board with squares in the bottom row and in the top row, located as shown shown in the figure.
https://cdn.artofproblemsolving.com/attachments/f/3/516ad5485c399427638c3d1783593d79d83002.png
In the bottom row the integers numbers from to are placed in some order. Then in each box in the top row records the multiplication of the two numbers below it. How can they place the numbers in the bottom row so that the sum of the numbers in the top row be the smallest possible?