Pentominous sandwich sudoku
(Eingestellt am 28. April 2021, 17:11 Uhr von Nylimb)
This is a combination of a pentominous puzzle and a sandwich sudoku.
Standard sandwich sudoku rules apply: Fill the grid with digits from 1 to 9, so that every row, column, and 3x3 box contains each of the 9 digits exactly once. A number next to a row or column gives the sum of the digits between the 1 and the 9 in that row or column.
Also, divide the grid, without the central grey cell, into 16 pentominoes, so that 2 pentominoes of the same shape never share an edge, even if one is a rotation or reflection of the other. (Not all of the 12 pentomino shapes need to occur.)
The sudoku and pentominous solutions are related in two ways:
First, in each row and column, the cells of the sandwich filling (i.e. the numbers between the 1 and the 9) are all in the same pentomino, but the 1 and 9 are not in that pentomino. The 1 and 9 may be together in a pentomino, as long as it doesn't contain any cell in the filling.
Second, a digit cannot repeat within a pentomino.
The first figure below shows all 12 shapes of pentominoes, along with their standard names.
The second one shows a valid pentominous sandwich sudoku grid. For example, in row 1 the sandwich filling has 7, 2, 3, and 4. These sum to 16 and are all in the same Y-pentomino, but the 1 and 9 in the row are not in the Y. In this row the 1 and 9 are in different pentominoes, but columns 8 and 9 show two ways for the 1 and 9 to be in the same pentomino. Every pentomino in the grid contains 5 different numbers.
Here is the actual puzzle:
You can solve this in the CTC-app.
Lösungscode: List the shapes of the pentominoes that contain the 9 cells in column 6 (from top to bottom), followed by the digits in the column. (That's 9 letters and 9 digits.) E.g. for the sample grid shown earlier, the solution code would be YFFPPPXTL481265937.
Kommentare
am 25. Februar 2024, 03:58 Uhr von Nylimb
Added CtC-app link.
am 24. Februar 2024, 22:58 Uhr von Nylimb
Added warning about broken penpa link.
am 10. August 2021, 20:02 Uhr von uvo_mod
Labels angepasst.
am 22. Juni 2021, 15:38 Uhr von Mody
Tolle Konstruktion. Schon die Pentomino-Verteilung muss ziemlich schwierig gewesen sein.
Great construction. The pentomino distribution alone must be quite difficult.
@Mody: That's true. Most positions for the 1's and 9's don't allow pentominous dissections. Of those that do, most have too many dissections, and in most cases some of the 1's and 9's could be swapped. Once I chose a particular set of 1 and 9 positions, I did a lot of experimentation with possible sandwich sums to find one that led to a unique solution.
am 10. Mai 2021, 23:46 Uhr von RockyRoer
Enjoyed this very much once I broke out the colored pencils. I've never been able to do a Pentominos puzzle, so I was thrilled when I managed to finish! Thanks for setting it!
am 29. April 2021, 12:02 Uhr von marcmees
very nice puzzle. crusts of the sandwich easily found, but definitely more intriguing path to disclose the shapes of the pentominoes.thanks
am 29. April 2021, 09:12 Uhr von henrypijames
Difficult but linear, therefore never felt stuck - except when I made a mistake and had to debug, which took quite a while.
am 29. April 2021, 00:44 Uhr von MagnusJosefsson
Very nice, interesting through all the phases. I liked the ending!
@MagnusJosefsson: Thanks, I like it too. It took many tries to come up with a puzzle that had a unique solution. Luckily, when I finally did it turned out better than I had hoped for.
am 28. April 2021, 17:12 Uhr von Nylimb
Added "sandwich" tags.
