Hi guys,
Help...!!!
Prove by induction why a "3 by odd" tiling of trominoes won't work.
Also, prove by induction why a 2^k by 2^k tiling of trominoes WOULD work.
Hello, harold!
Prove by induction why a "3 by odd" tiling of trominoes won't work.
Also, prove by induction why a 2^k by 2^k tiling of trominoes WOULD work.
If a tromino is a three-unit polyomino (as defined by Solomon W. Golomb),
. . there are two possible shapes.Code:*---* | | * - *---* *---*---*---* | : | | : : | *---*---* *---*---*---* "L" "I"
I must be missing something . . . I don't understand the questions.
A "3 by odd" can be tiled with a number of I-trominos.
And a "2^k by 2^k" region has 4^k square units
. . which can not be a multiple of 3.
I'm not sure either...this is a page that talks about trominoes and gives some induction but I still don't get it...
A Geometric Induction Example: the Tromino Puzzle
Hello again, Harold!
It would have helped if you had explained the problems clearly.
First of all, we're limited to the L-shaped tromino.
Secondly, for the tiling of a "2^n by 2^n" square, you neglected to tell us
. . that one unit square is already covered.