2024x2023 rectangle is filled with 3 types of pieces
Source: Moldova JTST 2024 P11
June 10, 2024
combinatoricsrectangle
Problem Statement
A rectangle of dimensions is filled with pieces of the following types:
[asy]size(200);// Figure (A)
draw((0,0)--(4,0)--(4,1)--(0,1)--cycle);
draw((1,0)--(1,1));
draw((2,0)--(2,1));
draw((3,0)--(3,1));// Figure (B)
draw((6,0)--(8,0)--(8,2)--(6,2)--cycle);
draw((7,0)--(7,2));
draw((6,1)--(8,1));// Figure (C)
draw((10,0)--(12,0)--(12,1)--(11,1)--(11,2)--(9,2)--(9,1)--(10,1)--cycle);
draw((10,0)--(10,1));
draw((11,0)--(11,1));
draw((10,1)--(11,1));
draw((9,1)--(9,2));
draw((10,1)--(10,2));
draw((11,0)--(12,0));
draw((10,1)--(12,1));// Labeling
label("(A)", (2, -0.5));
label("(B)", (7, -0.5));
label("(C)", (10.5, -0.5));[/asy]
Each piece can be turned arround, and each square has side length .
Is it possible to use exactly 2023 pieces of type ?