## Monday, May 7, 2012

### No fault lines

Build a rectangle with multiple 2x1 bricks such that the rectangle has no "fault lines".  A fault line is a straight line through the rectangle that does not cut through any of the bricks.

For example, the following rectangle fails because of the fault line indicated in red.
What's the smallest rectangle you can make without fault lines?  You may send solutions to skepticsplay at gmail dot com.

Can you do the same with 3x1 bricks?

This puzzle is taken from Polyominoes: Puzzles, Patterns, Problems, and Packings, by Solomon W. Golomb.

See solutions

Anonymous said...

a single 2x1 brick

miller said...

But you need to use multiple bricks.

Anonymous said...

Three.

miller said...

More than three are necessary. If you need to verify a solution you can send it to me.

blahs said...

I wanna say 5x4...

miller said...

It's not enough to guess the best size, you have to construct a solution! 5x4 is not possible.

Eduard Baumann said...

aabbc
bccac
bddab
caccb
cabaa
ddbcc
is a 5x6 case. Smallest?

miller said...

Yes, 5x6 is the smallest possible solution! I believe there are other unique forms though.

midori said...

Oh hey, 5x6 is the smallest? I found a 5x6 solution.

No, nevermind, now that I look closely it's just like Eduard Baumann's solution, only flipped.

D2000 said...
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D2000 said...

A B C C D D
A B E F F G
H H E I J G
K L L I J M
K N O OM