## Puzzle 13: Prime/Composite Fillomino

This is a fillomino with the extra restriction that all prime-sized regions are contiguous and all composite-sized regions are contiguous (1s don’t matter).

Notes: Thanks to Cy Reb, Jr. for the original concept.

I think many more cool things can be done with this kind of variation (several groups of polyominoes needing to be contiguous), and this puzzle isn’t very interesting when it comes to creatively using the condition, but I hope you all enjoy it anyways.

Thanks! I liked solving your puzzle, and this showed some things not entirely obvious from my pitch, like both big and small reveals.

Bryce HerdtNovember 9, 2011 at 1:10 am

I am not sure if i understand “1s dont matter”.Hope it does not mean you can link pieces of same family through the 1s.

Anuraag SahayNovember 27, 2011 at 6:05 am

It means 1’s don’t need to connect to anything in particular; they can just be present.

Bryce HerdtNovember 28, 2011 at 6:41 pm

Er, that didn’t answer your worry. So I mean, no, 1’s never connect to anything. They block the connectivity of both the primes and the composites. The have to be worked around.

Bryce HerdtNovember 28, 2011 at 9:10 pm

as i expected. But where is the solution? It does not fall to any logic yet i am afraid

Anuraag SahayDecember 2, 2011 at 4:06 pm

Replying here because the comment I mean to answer doesn’t have a “Reply” link….

The 1’s only confound the analysis a little, so let’s ignore them for a bit. The first thing to look for in two-region puzzles like this is the perimeter squares, which form a loop. There’s a composite, 8, and three primes on the perimeter here, so this loop must be shared by the two regions. The only consistent way to do that is to divide it into two sections, one of composites and one of primes, because the regions can’t cross. (For example, such a puzzle can’t be solved if there are composites on the top and bottom edges and primes on the left and right edges.)

Technically, the number of perimeter regions is increased with the addition of 1’s, but even though the 1’s might interrupt a stretch of composites, the primes can’t. Neither can some composites interrupt a stretch of primes.

So the way to start the puzzle is to figure out how the composites in rows 1 and 9 connect, as well as the primes in rows 2 and 10.

Bryce HerdtDecember 4, 2011 at 5:30 am