Puzzle 28: Mashed Fillomino and Special Puzzle 6: Just Can’t Get A Clear Sky

UPDATE: Here is a new Puzzle 28, 5 months after the original. Yeah.

After a smoothie, I serve a mashed potato—err, a mashed Fillomino.

Fillomino Epic Variation. No less than four variations that made an appearance in the original Fillomino Fillia are in this puzzle: Shape, Even-Odd, Greater Than, and Sum. Follow usual Fillomino rules. In addition, the given shapes must appear in the grid without rotation (because I apparently forgot this rule when constructing, let be so), all even numbers are connected in a single polyomino and so are for odd numbers, all inequality signs must be followed by the numbers in the respective cells, and the sum of the numbers in each cage must match the given. Calling MellowMelon for a better presentation.

Puzzle 28: Mashed Fillomino
Fillomino (Epic Variation)
(click to enlarge)

UPDATE: Ambiguity acknowledged. Assume R2C2 and R3C2 have different numbers. I will soon replace the puzzle with another one which should be similar (S,H,A,P,E shapes and a certain gimmick) but better made. Most likely I’ll use givens as opposed to sum cages and greater than signs…maybe.

So, yeah. My take at a Potpourri; MellowMelon made an extremely hard one that I haven’t solved 1.5 years ago and the post is linked above.

ksun48 solved Puzzle 25, and he asked for a “hard Fillomino variation”. I hope this is sufficiently hard, since otherwise I have a harder puzzle…

Special Puzzle 6: Just Can’t Get A Clear Sky
Fillomino Epic Variation [Count Solutions]

So, what’s the puzzle? You are given a 11×11 grid of Fillomino, and the five shapes as above. The only variations applied are Shape and Star (each row/column must have two stars occupying the space of a monomino each; no two stars are adjacent even diagonally). Count the solutions, and prove it.

I guess the title helps you in some way, but you still need to prove it. Yay.

In case you missed it, I served a smoothie (Puzzle 27) a few seconds ago.

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