Samurai Star

One of my favourite Samurai Sudoku arrangements is the Samurai Star, also sometimes known as Flower Samurai.  There’s been one every month in Sudoku Pro magazine for years, and what’s great about them is that because of the tight overlap of the underlying 9×9 grids there is some ‘new’ logic you can apply – essentially if a number occurs in a 3-cell row or column within a 3×3 box then that same number must also occur in the 3-cells that start 9 to the right/left/above/below (depending on whether it’s a 3-square row or column).  It might sound confusing but it’s much more obvious when you try it out on an actual puzzle, and it’s one of those things that makes you go “ah, that’s nice” as you solve a puzzle – which is a good indicator of a decent design!

This particular puzzle has ‘8-way’ symmetry, which simply means that the pattern of givens is the same when reflected in both diagonals, and when rotated any multiple of 90 degrees, and when reflected and rotated.

The rules are simple: place 1 to 9 into each of the rows, columns and 3×3 boxes of the five underlying 9×9 Sudoku grids – four of them are obvious, and then there’s one in the centre too.  It’s this centre grid that leads to the property I talk about above!  You won’t find a unique solution if you omit this additional grid.