Consecu-doku is a variant of classical Sudoku. It still involves rows,
mini-boxes and as usual, digits 1 through 9 must exist in all of them
Unlike classical Sudoku, Consecu-doku grids contain circles between some adjacent
cells. Those circles indicate that the numbers in those cells must be
(ascending or descending).
Also, the numbers in adjacent cells that do not have a circle CANNOT be consecutive.
These puzzles can be solved using the typical Sudoku solving techniques (ie. hidden
singles, naked singles, hidden doubles, triples, etc). They can be solved without
resorting to advanced strategies such as X-wings, XY-Wings ,Swordfish, etc.
Here are a few tips to get you started:
Tip #1 Look at solved cells and "givens"
Cells adjacent to solved or given cells will eliminate candidates as shown here:
Tip #2 Look for cells with 2 circles
Cells with two circles on opposite sides cannot contain a 1 or a 9
The digit 1 can only be consecutive with digit 2. Since it is not possible to have
two 2's in the same row, digit 1 is not possible in the center cell. Similarly, digit
9 can only be consecutive with digit 8. So 1's and 9's are not possible in cells
with two opposite circles.
When a cell has two circles not opposite to each other ("L" shaped), these cells
also cannot be 1 or 9 if the cells reside in the same box).
In the example below, the three adjacent cells do not reside in the same box.
In this case 1's and 9's are still possible.
Tip #3 Look for cells that are missing 2's or 8's
When a cell is missing a 2, adjacent cells with circles
cannot contain a 1
Cells with missing 8's will remove 9's from adjacent cells with circles
Tip #3 Look for bivalue cells with consecutive values
Bivalue cell have only two candidates remaining. If they are consecutive,
they will eliminate those candidates from adjacent non-circled cells.
The pair in the center cell (45) are consecutive which allows removal of
those candidates from adjacent cells with no circles. Also note how the pair
affects the adjacent circle cell to the left. The candidates in that cell must be
within -1 below or +1 above the pair, otherwise they are eliminated.
Tip #4 Think "parity" (ie. even or odd)
Consecutive cells must have opposite parity. If all candidates in a cell are odd,
candidates in adjacent circled cells must be even (and vice versa)
Note how the candidates alternate between even and odd in the adjacent circled cells.
Tip #5 Look for hidden singles
A hidden single is found when a number exists in only one cell of a row, column, or box.
Candidate 8 exists only once in box 6. It causes multiple eliminations
as shown (it also solves the cell to the left which becomes a 9. Hidden
singles can be hard to spot but they will be frequent finds.