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.