1 x 3 pieces in a 3 x 25 board,m max no of pieces placed
Source: Lusophon 2018 CPLP P6
September 13, 2018
combinatoricscombinatorial geometrymaximum
Problem Statement
In a board, pieces are placed (vertically or horizontally) so that they occupy entirely boxes on the board and do not have a common point.
What is the maximum number of pieces that can be placed, and for that number, how many configurations are there?[hide=original formulation]
Num tabuleiro 3 × 25 s˜ao colocadas pe¸cas 1 × 3 (na vertical ou na horizontal) de modo que ocupem inteiramente 3 casas do tabuleiro e n˜ao se toquem em nenhum ponto.
Qual ´e o n´umero m´aximo de pe¸cas que podem ser colocadas, e para esse n´umero,
quantas configura¸c˜oes existem?
[url=https://www.obm.org.br/content/uploads/2018/09/Provas_OMCPLP_2018.pdf]source