Wednesday 16 December 2015

grid deduction - Tetromino Sudoku



An entry in Fortnightly Topic Challenge #32: Grid Deduction Hybrids




The grid below, when filled in, forms a valid Sudoku grid. It can also be filled in like a LITS (nuruomino) puzzle without the 1x4 tetrominos.


The two objectives of this puzzle are:



  • Fill in the numbers in the grid.

  • Identify the LITS tetrominos.


grid


In addition to the standard rules of Sudoku and LITS, the following rules apply:




  • Each 3x3 region in the Sudoku grid contains exactly one tetromino, which is either a L, T, or S tetromino.

  • The tetrominos obey the rules of a LITS puzzle.

  • The shaded yellow spaces are part of a tetromino.

  • Each tetromino contains four numbers that add up to 20.

  • No two tetrominos may contain the same set of four numbers.

  • The tetrominos (each in its own 3x3 region) are arranged in a 3x3 Sudoku, using tetromino shapes L, T, and S instead of numbers. If two regions contain the same tetromino shape, then they cannot share the same horizontal alignment or vertical alignment.


Good luck!



Answer




I believe I have found multiple solutions to the puzzle. It is possible that there is a nuance to the rules that I missed that disqualifies one or both of them. My understanding of the rules did not allow for a full logical deduction of the solution, so these were both found by brute force.


The sudoku is on the left, while the tetrominoes are on the right:



951 837 426 42
376 542 918 37 4 9
428 916 573 28 916 5

532 678 149 3 6 4
147 329 685 47 329 68
869 154 237 6 2

683 491 752 83 91 752
794 285 361 4 28 6
215 763 894 5




The lower-center tetromino can be flipped to:



. 1
. 85
. 6



hence the multiple solutions.


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