# Math Help - Trominoes Induction Pf?

1. ## Trominoes Induction Pf?

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.

2. Originally Posted by harold
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.
You had better tell us what you mean by trominoes, and what
restrictions there are on how you do the tillings.

RonL

3. 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.

4. 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

5. 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.

6. Sorry bout that Soroban...I didn't know myself--new territory for me. I see what they're getting at with the discussion about the induction but how do I formally write it out for both cases??