rectangle 15 x n from specific pieces - Chile 2002 L2 P2
Source:
September 1, 2022
geometryrectanglecombinatoricscombinatorial geometrychilean NMO
Problem Statement
Determine all natural numbers for which it is possible to construct a rectangle of sides and , with pieces congruent to:[asy]
unitsize(0.6 cm);draw((0,0)--(3,0));
draw((0,1)--(3,1));
draw((0,2)--(1,2));
draw((2,2)--(3,2));
draw((0,0)--(0,2));
draw((1,0)--(1,2));
draw((2,0)--(2,2));
draw((3,0)--(3,2));draw((5,-0.5)--(6,-0.5));
draw((4,0.5)--(7,0.5));
draw((4,1.5)--(7,1.5));
draw((5,2.5)--(6,2.5));
draw((4,0.5)--(4,1.5));
draw((5,-0.5)--(5,2.5));
draw((6,-0.5)--(6,2.5));
draw((7,0.5)--(7,1.5));
[/asy]The squares of the pieces have side and the pieces cannot overlap or leave free spaces