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.

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- Sep 29th 2006, 09:48 PMharoldTrominoes 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. - Sep 30th 2006, 12:23 AMCaptainBlack
- Sep 30th 2006, 10:33 AMSoroban
Hello, harold!

Quote:

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.

- Sep 30th 2006, 10:40 AMharold
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 - Sep 30th 2006, 04:17 PMSoroban
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.

- Oct 1st 2006, 03:14 PMharold
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??