Dr. Sudoku Prescribes #62 – Sudoku (Seek and Spell)
or solve online (using our beta test of Penpa-Edit tools)
This is a “Franken-Friday” puzzle variation.
Theme: Mostly Themeless! – Besides elements of symmetry and some patterning in the numbers, the design is focused on the logical solution path.
Rules: Standard Sudoku rules. Clues in the grid represent typical “Seek and Spell/Kanaore” clues; specifically, it must be possible to read each of the numbers listed below the grid by starting at the indicated letter, moving one cell in the direction indicated by the arrow, and then continuing to move one cell at a time up, down, left, or right to complete the number. No cell may be used more than once in a single number’s path, but the same cell can appear in the paths of different numbers.
Answer String: Enter the 3rd column from top to bottom, followed by a comma, followed by the 9th column from top to bottom.
Time Standards (highlight to view): Grandmaster = 7:00, Master = 12:30, Expert = 25:00
Solution: PDF
Urgh. I botched my solve the first time around and had to restart.
I had a number of botches, but I managed to fix them without restarting. This is a nice variant. You could also pair it with snake rules (ie the snake can’t touch itself even diagonally) for some more flair.
I know in this particular puzzle, the final number paths were uniquely determined, but is that a requirement of the rules? For example, if you had to place 1234 on a path, is it possible that the solution will have:
1234
4
erg, I thought the code tag would allow whitespace…
should be:
1234
.34
So you can read 1234 in 3 different ways (RRR, RRD, RDR).
I’ve never noticed a Kanaore with such an ambiguity but I see no reason the rules wouldn’t allow it. Particularly here, in a setting where other properties of the grid can fill in the remaining cells, I don’t believe the “unique path” constraint needs to be as strong.
In some ways, I’d say the non-uniqueness of components does not diminish the uniqueness of the whole. In a No Operation TomTom you can have a cage that is one in a set of possible operations. But the overall solution is always the same. That has never bothered me, but I remember some early commenters wondering if I should say something like “every operation is used at least once” to resolve uniqueness in that case. Obviously that can’t work all the time, and making the operation assignments resolve uniquely is not a goal I’ve ever bothered with.
On the other hand, requiring there to be one and only one path for each word opens up additional possibilities for deductions.
Codifying a rule so that “uniqueness” is now the desired type of deduction feels sort of odd to me.
Here again I’m reminded of past discussions. I made some diagramless puzzles (also TomToms) several years ago and made sure they had only one grid assignment that had any solutions and only one solution in that grid assignment. Someone else critiqued my approach and said I was missing the opportunity to have other grids have far too many solutions so that “uniqueness of solution” was what had to be discovered. I was not moved by the discussion. It seemed to be a bug and not a feature to design things that way.
Hmm, but wouldn’t a unique path be closer to the single loop requirement of slitherlink than to the unique puzzle solution requirement of a blank-grid puzzle? In other words, the uniqueness in this case is a feature of part of the solution rather than size of the set of valid solutions.
Not as I see it based on your example. Say the path (for its last digit) could go down to a placed 3 or over to another box to an unplaced digit that could be 3. Having a requirement of a unique path suddenly excludes a 3 in a spot that otherwise could have had any number including 3. This is exactly what reduces solution count in a placement puzzle and in this case it seems arbitrary to a “uniqueness” requirement.
I can’t think of a similar situation in a Slitherlink that reduces otherwise unconstrained puzzle space. The single loop requirement is more like the “don’t repeat any digit” requirement in that it is global and uniform. The Seek and Spell rule is local and multiple clues interact together, which is why it need not be as strict.
We may be revisiting this concept next week with another puzzle that has an extra rule that is certainly satisfied by the solution uniquely, but is not itself unique in the solution. You’ll know it when you see it.
15:43
Initially i was under the impression that the 4 series of numbers given would fill the entire cells.
Realised my stupidity in the middle when it suddenly hit me that ‘how can 36 numbers fill 81 cells’??
Nice puzzle!!
Wow, this was a pretty good puzzle (coming from someone who hates sudoku generally)
Thanks. My job is to help the sudoku medicine go down.
I guess I’m missing something here (n00b). If I read the directions correctly, R6C6 is 7, R7C6 is 8 as given. R9C8 is 4, R8C8 is 2 – now we have to fill in the 818, but there’s no way for that to happen without duplicating the 8 somewhere (how do you cross R7 and shift diagonally). Are you allowed to wrap as well? Thanks – these puzzles are awesome!
The paths can cross, so it is possible one of the 8’s in “818” is the one you placed in R7C6.
I really enjoyed the “seek and spell” opening, (I’ve never seen a puzzle of that type before). I was almost done with the seek-and-spell portions, (just one digit left in each of two of the “words”), when I paused for an excessively long time. After searching and searching I finally realized that there was a digit that only had one available cell in the lower-right region. I’m terrible at being blind to things like that in sudoku. Once I put that in place, all the rest fell together quite nicely.
So this probably would have been a perfectly lovely puzzle for anyone who doesn’t have massive Sudoku blind spots like I do.