2
Part of 2019 May Olympiad
Problems(2)
min sum of 2-products in top row May Olympiad (Olimpiada de Mayo) 2019 L2 P2
Source:
9/24/2021
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?
combinatorics
Chess tournament
Source: May Olimpiad 2019 L1 P2
3/10/2021
More than five competitors participated in a chess tournament. Each competitor played exactly once against each of the other competitors. Five of the competitors they each lost exactly two games. All other competitors each won exactly three games. There were no draws in the tournament. Determine how many competitors there were and show a tournament that verifies all conditions.
combinatoricsnumber theory