Logic Masters Deutschland e.V.

Tiling Pentomino Sandwich Sudoku

(Eingestellt am 7. August 2020, 12:51 Uhr von psams)

Penpa Version Playable Online


The grid consists of a 9x9 Sudoku plus a row and column of sandwich clues.

Standard Sudoku rules apply. Sandwich clues specify the sum of digits between the 1 and the 9 along a row, column, or diagonal indicated by a small arrow.

  • Tile the full 10x10 grid using only F-type pentominoes in four colors: Blue, Green, Red, Yellow, matching the pre-colored cells.
  • Some Pentominoes wrap around the edges of the 10x10 grid, from top to bottom or from left to right.
  • Pentominoes of the same color must have the same exact orientation and may not touch orthogonally or diagonally.
  • Pentominoes of different colors must have different orientations.
  • The solution tiling is periodic and rotationally symmetric.
  • The sum of the numbers in each Blue pentomino is even, including sandwich clues.
  • Pentomino centers may land upon given sandwich clues. These givens must not be changed. After tiling, number any unnumbered center cells of each pentomino according to its color (Blue 9, Green 7, Red 4, Yellow 8).
  • Sudoku digits other than 1 or 9 may repeat along the diagonals.

Here is an example of legal F type pentominoes. Note the numbers placed in the center cells may be Sudoku digits or Sandwich clues.

It is possible to tile an infinite plane with any of the 12 pentominoes. Here is an example of tiling that obeys the rules above using P-type pentominoes:

Puzzle Series

Lösungscode: Row 5, Column 7 of the Sudoku (18 digits total)

Zuletzt geändert am 18. August 2020, 13:13 Uhr

Gelöst von bosjo, davidagg
Komplette Liste


am 18. August 2020, 16:30 Uhr von psams
@bosjo Thank you for your generous comment. Sometimes the solvers find options the setter missed! I could disambiguate the tiling, but I think I will leave it unchanged for those looking for a challenge.

If your first tiling fails the sudoku, try again, but not more than twice!

am 18. August 2020, 15:58 Uhr von bosjo
The tiling bit is the difficult part — I found three ways of getting the tiles with the correct colours; two of them were hopelessly broken when adding the center digits, and the third I thought was broken when I couldn't put a certain digit on the diagonal. With that misunderstanding cleared up, it was fairly straight forward from that point.

A nice puzzle, but with a few unusual and unclear details in the initial description. I particularly liked the "double impossible ending", resolved by one of the innocent looking requirements. I spent a long time trying to solve this, but I guess the author spent far more making this intricate machinery work.

If you like pentominoes, which I do (or at least did...), then you have to try this puzzle!

am 18. August 2020, 13:13 Uhr von psams
Increased difficulty rating.

am 18. August 2020, 13:07 Uhr von psams
Clarified rules.

Zuletzt geändert am 7. August 2020, 15:01 Uhr

am 7. August 2020, 15:00 Uhr von RockyRoer
What are the bigger numbers along the bottom and right side? Sums of centers? Nevermind... see it now... sandwich clues.

Gelöst:2 mal
Beobachtet:6 mal

Rätselkombination Rätselvariante Färberätsel Pentominos

Lösung abgeben