Each row and column must contain the digits 1-9. Digits may not repeat within the outlined regions. Digits may not repeat in cells of the same colour (except white). Digits outside the grid in red are colour sums. The value is the sum of all coloured cells (i.e. non-white) in that row / column. Digits outside the grid in black are sandwich clues. The value is the sum of all digits in that row / column between the 1 & 9.
Normal sudoku rules apply. Additionally, Kropki dots are placed in the grid. Kropki rules are applied only along the grey line (orthogonally or diagonally): adjacent cells containing digits whose difference is 1 are marked with a white circle; adjacent cells containing digits whose ratio is 2 are marked with Black circle; adjacent cells containing digits 1 and 2 may be marked with white or black circle. Adjacent cells with no marking must not contain digits whose difference is 1 or whose ratio is 2.
Mark Goodliffe and Simon Anthony from cracking the cryptic are doing a fantastic job of making us discover the fascinating world of advanced sudoku.
Here is a treat for the season: normal sudoku rules apply, and identical digits cannot be a chess knight’s move apart. The grey square marks an even digit. Any two cages that share an edge and whose totals have a difference of 1 have a white dot between them, and any two cells that share an edge whose totals have a ratio of 2:1 have a black dot between them; there is a negative constraint so two cages touching each other without a dot do not have totals with a difference of 1 or a ratio of 2:1.
Please try the puzzle here.