I have not posted anything for several weeks now, and in fact I did not have much time for setting or solving puzzles lately. Still, I somehow felt the urge to continue with our current Sudoku series. Two new sets are just complete now, which means this is the first part of a “double feature”. Here is today’s PDF file: Even/Odd Sudoku
Rules: Enter numbers from 1 to 6 (1 to 4 in the example) so that each number appears exactly once in every row, every column and every outlined region. Cells with grey squares must contain even numbers. Cells with grey circles must contain odd numbers.
Example and solution:
To be quite frank, Even/Odd Sudokus are not what I would call an exciting variant. That is because Even/Odd clues do not contribute any additional element to Sudoku. This variant belongs to the category of Candidate Sudokus, i.e. the clues only limit the set of candidates for the respective cell, a concept which is already present in Standard Sudokus. As such, they do not bring forth any new solving techniques.
Nevertheless, they appear to be somewhat popular; I guess this has to do with the simplicity of the rules. By the way, when I designed Even/Odd Skyscrapers a long time ago, I used to denote clue cells with small letters E and O (or G and U for the German designations). I prefer the layout with grey squares and circles, which is highly intuitive and also much easier to survey, unless this variant is combined with another which also uses grey symbols.
Regarding puzzle theory, I would like to briefly mention that N-2 givens are needed in this variant (where N denotes the grid size). That is because the different entry values are interchangeable only as long as the parity is preserved. Therefore, in each group – Even and Odd – all numbers but one must be given from the start for the solution to be unique.
In practice, easy Even/Odd Sudokus tend to be solvable using Naked and Hidden Singles only (similar to Standard Sudokus, although the clues may be necessary for the Singles to emerge). More difficult specimens may require the corresponding harder techniques. Since the candidate structures are mostly based on the Even/Odd clues, so are the solving steps.
It is not uncommon that the first part of the solving part consists of entering only further squares and circles, covering a significant part of the grid, before even a single number can be located. In that case, the last part of the solve typically breaks down into two rather independent pieces, namely solving the Even half of the Sudoku and solving the Odd half.
As usual, I have tried to design the six Sudokus from our set so that the difficulty is increasing. The first few puzzles contain nothing deep, it may just be a little harder at certain occasions to spot the next step. If you need any help with the last puzzle, feel free to highlight the following paragraph to obtain a small hint.
Hint: The two cells R6C1 and R6C2 must contain the same entries as R5C4 and R5C6. All three locations of even numbers in Column 4 are thus known, and the parity of several more entries can be marked. In fact, it is possible (although not strictly necessary) to take it from there and divide the entire grid into Even and Odd cells before entering any numbers.
As I said earlier, this set is not really thrilling. But I hope you enjoy the puzzles nonetheless, and stay tuned – the next installment of our series is supposed to be coming soon.