As promised only a few days ago, the next puzzle set is ready; I guess we will take a longer break again now. There are several more variants I intend to incorporate into the Sudoku Compilation – I am not sure exactly how many, just that it is too early to bring this series to an end. In any case, I have a feeling that I will do some very different things over the remaining summer months. Never mind, here is the PDF file: Next To One 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. A clue outside the grid indicates which numbers are adjacent to the entry 1 in the respective row/column. (In that case all numbers are given, i.e. a single number clue indicates that there is only one number adjacent to 1.)
Example and solution:
This is the first variant in the Sudoku Compilation featuring clues outside the grid which restrict the contents of a row or column. Some others of the same category are X-Sums Sudoku or Sandwich Sudoku. Those, however, are much harder to handle on a 6×6 grid, since they are based on arithmetic techniques which are severely limited with fewer numbers available.
Before creating this set, I barely had any experience with the variant, and I actually struggled a lot to come up with six interesting puzzles. (You will note, for example, that the first two puzzles have very similar break-ins.) Maybe it has to do with my reluctance to use any givens; as with a lot of variants, I prefer to work without givens if they are not needed for uniqueness.
All in all, I felt that the rules have very little potential for exciting solving steps, and that most of what I did here was repetitive, to say the least. And still, I was warming up to the variant while I kept going. You will find (I hope) that the last few puzzles contain some beautiful tricky steps; even if the hard Sudokus in our set can once again be solved much faster using bifurcation, it is worth exploring the logic in them. Below you will find a hint for the sixth puzzle on the PDF sheet.
Hint: Study the possible locations of the entry 1 in Column 6, and in particular the Candidates for the cells R3C6 and R4C6. After that, examine which cells in Column 4 can accommodate the number 6.
By the way: When you encounter today’s variant on a 9×9 grid in an event, it is often called “Next To Nine Sudoku” instead (with the instructions adapted accordingly). The problem is that, if the clues indicated which entries are adjacent to the largest number, the puzzle designation would have to be adjusted every time the grid size changes. I believe it is desirable to have a uniform name for all possible sizes, which is why I prefer to use the “Next To One” version here. Anyway, enjoy the puzzles!