UT Math Club Problem of the Month
October 13, 2009
Problem I (The Trouble with Turner’s Tiles) American media tycoon Ted Turner
is tiling his bathroom floor. The floor is a perfect rectangle and he tiles
it using a combination of 2 × 2 and 1 × 4 tiles. Just as he finishes and
stands back to survey his work, wacky Australian-born global media
mogul Rupert Murdoch jumps out from behind Turner and smashes one
of the tiles in the floor, leaving all the other tiles undamaged. Laughing
maniacally, Murdoch runs off into the mist, leaving poor Turner with an
unfinished bathroom floor. Unfortunately, Turner only has one spare
tile, and it is of the opposite kind that Murdoch smashed. Can Turner
complete the job of tiling his bathroom by using his spare tile and
possibly rearranging the tiles that are already on the floor?
Problem II (Triangles) There are n points given in the plane satisfying the property
that any three of the points form a triangle of area less than or equal to
1. Show that all n points are contained in a triangle of area less than
or equal to 4.
Submission Deadline: Friday, October 30 by 11:59 PM
1