Floor Tiling
Source:
November 26, 2009
Problem Statement
The diagram represents a -foot-by--foot floor that is tiled with -square-foot black tiles and white tiles. Notice that the corners have white tiles. If a -foot-by--foot floor is to be tiled in the same manner, how many white tiles will be needed?
[asy]unitsize(10);
draw((0,0)--(7,0)--(7,7)--(0,7)--cycle);
draw((1,7)--(1,0));
draw((6,7)--(6,0));
draw((5,7)--(5,0));
draw((4,7)--(4,0));
draw((3,7)--(3,0));
draw((2,7)--(2,0));
draw((0,1)--(7,1));
draw((0,2)--(7,2));
draw((0,3)--(7,3));
draw((0,4)--(7,4));
draw((0,5)--(7,5));
draw((0,6)--(7,6));
fill((1,0)--(2,0)--(2,7)--(1,7)--cycle,black);
fill((3,0)--(4,0)--(4,7)--(3,7)--cycle,black);
fill((5,0)--(6,0)--(6,7)--(5,7)--cycle,black);
fill((0,5)--(0,6)--(7,6)--(7,5)--cycle,black);
fill((0,3)--(0,4)--(7,4)--(7,3)--cycle,black);
fill((0,1)--(0,2)--(7,2)--(7,1)--cycle,black);[/asy]