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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 3×253 \times 25 board, 1×31 \times 3 pieces are placed (vertically or horizontally) so that they occupy entirely 33 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