1. Can a 7×7 square be tiled with the two types of tiles shown in the figure? (Tiles can be rotated and reflected but cannot overlap or be broken)2. Find the least number N of tiles of type A that must be used in the tiling of a 1011×1011 square. Give an example of a tiling that contains exactly N tiles of type A.
[asy]
size(4cm, 0);
pair a = (-10,0), b = (0, 0), c = (10, 0), d = (20, 0), e = (20, 10), f = (10, 10), g = (0, 10), h = (0, 20), ii = (-10, 20), j = (-10, 10);
draw(a--b--c--f--g--h--ii--cycle);
draw(g--b);
draw(j--g);
draw(f--c);
draw((30, 0)--(30, 20)--(50,20)--(50,0)--cycle);
draw((40,20)--(40,0));
draw((30,10)--(50,10));
label((0,0), "(A)", S);
label((40,0), "(B)", S);
[/asy]
Proposed by Muralidharan Somasundaran TilingcombinatoricsColoringEgmo tst