Est. 1998 — 27 years of woodworking knowledge
Let's try a slightly harder one
And slow down, Gary! ;-)
A 12'x12' room can be tiled with 72 1'x2' tiles without cutting any tiles.
If the NE and SW corners of the room have a 1'x1' column taking up the corner, can the remaining 142 sqft of floor be tiled with 71 1'x2' tiles? How, or why not?
Re: Let's try a slightly harder one
Isn't this a classic weaving pattern?
I'm not familiar with classic weaving pattern
Herringbone
Herringbone won't work
Impossible
Here's why:
Color the floor of the 12x12 room like a checkerboard, with 1'x1' squares. There will be 72 white squares and 72 black ones. The squares along any diagonal are the same color, so when we remove the NE and SW corner squares, we are removing two black [or two white] squares. So the room now has 70 black squares and 72 white ones. But any 1'x2' tile will cover 1 black and one white square. So there's no way for any combination of 71 1x2 tiles to cover 70 black and 72 white squares.
QED