An entry in Fortnightly Topic Challenge #52: Polyominoes.
This puzzle is a hybrid between Pentominous and Star Battle. Your job is to divide the grid below into pentominoes according to the rules of Pentominous, and then place stars in the grid according to the (slightly modified) rules of Star Battle. Specific to this puzzle:
- You must partition the grid into pentominoes such that:
- All cells are covered and no pentominoes overlap.
- No two pentominoes of the same shape (including rotations and reflections) are orthogonally adjacent.
- Each given letter in the grid must lie in a pentomino of the corresponding shape.
- You must also place stars in the grid such that:
- Each row and column contains two stars.
- Each pentomino contains ONE star.
- The star in each pentomino must be in a cell that is orthogonally adjacent to at least two other cells of the pentomino. So for example, the star in an X must go in the center.
- No two stars can be adjacent, neither orthogonally nor diagonally.
- Several star (★) locations are given in the puzzle. Stars may go in squares marked with pentomino letters.
I hope you enjoy!
SOLVER HELPS
Link to Penpa version
The pieces (adapted from Wikipedia):
TEXT VERSION
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| |★| | | | | | | |I|
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| | | | | | |Z| | | |
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|P| | | | | | |V|P| |
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| | |★| | | |Y| | | |
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| | | | |N|N| |★| | |
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| | | | |P|P| | | | |
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| | | |W| | | | | | |
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| |X|U| | | | | | | |
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| | | |L| | | | | |N|
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|L| | | | | |★| | | |
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Pieces:
FF
FF IIIII L NN
F LLLL NNN
PP TTT V
PP T U U V
P T UUU VVV
WW X ZZ
WW XXX Y Z
W X YYYY ZZ