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A few weeks ago, I challenged some people to solve the puzzle I made. Two of them took it more or less seriously, but couldn't find the right solution. Now they are excited to see whether or not anybody can do it by following the original instructions (translated to English here).

A sudoku is played on a 9x9 grid. The grid is further divided into 3x3 boxes. Each box as well as each row and each column must be filled by a player with 9 unique symbols from the set {1;2;3;4;5;6;7;8;9}. There is, by definition, only one suitable solution for a sudoku.

The grid below represents a partially hidden sudoku where the hidden cells are depicted as "W" whereas the cells marked "T" are empty before the player fills them.

The challenge is to find the single cell where a symbol can be written, without any risk of it being wrong, before the hidden part is revealed.

puzzle

So, I kindly ask you to write the correct answer along with some explanation to show, it isn't just a blind guess. If you find the puzzle incomprehensible, try explaining your reasoning anyway, just to see what people think about this challenge.

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  • $\begingroup$ Nice idea, but I wonder why neither of your two colleagues could solve it, as it is not a difficult puzzle. $\endgroup$
    – Weather Vane
    Commented Jun 3 at 12:54
  • $\begingroup$ @WeatherVane Orpnhfr gur fragrapr "Gurer vf, ol qrsvavgvba, bayl bar fhvgnoyr fbyhgvba sbe n fhqbxh." vf fvzhygnarbhfyl pehpvny naq rnfvyl bireybbxrq! $\endgroup$
    – Stef
    Commented Jun 3 at 17:05
  • $\begingroup$ @WeatherVane One of them apparently struggles with understanding all sorts of logic, and sometimes even admits that. The other one started finding examples, as if the W's and T's were not even different, then suspected that the text I wrote must have been wrong. Of course, they didn't try solving this full time, either. $\endgroup$
    – Paul Kolk
    Commented Jun 3 at 18:19
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    $\begingroup$ @PaulKolk Regarding the W and T, I do think replacing the T with just empty cells, and replacing the W by something that visually looks like it's obstructing the view, would make the puzzle more pleasing and easier to understand. As it stands I'm sure most people have to read the instructions several times to have a clear understanding of the difference between W and T; $\endgroup$
    – Stef
    Commented Jun 3 at 19:37
  • $\begingroup$ Also, I would consider moving the sentence (rot13 Gurer vf, ol qrsvavgvba, bayl bar fhvgnoyr fbyhgvba sbe n fhqbxh) to its own paragraph. The beginning of the paragraph is just the usual Sudoku rules that everyone knows, so readers will be tempted to just check quickly that the rules are the usual rules, and jump to the next paragraph without reading this paragraph in full, even though it contains a crucial instruction without which the puzzle in unsolvable. $\endgroup$
    – Stef
    Commented Jun 3 at 19:42

1 Answer 1

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I think the answer is

3 on R4C2.

Indeed

The other possible cell for 3 in the second visible box is R4C3, but it would create two distinct solutions for the sudoku (12 in R1 / 21 in R4 and 21 in R1 / 12 in R4)

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    $\begingroup$ I learned this technique from Cracking the Cryptic, but IIRC they also gave the impression that they don't like using it. I personally don't like using this technique either. It "feels bad" and doesn't feel like I am actually solving the puzzle. That doesn't make your solution any less valid, but is just an opinion of the puzzle, and OP said they were looking to see what people think about this challenge. $\endgroup$
    – mgarey
    Commented Jun 3 at 18:13
  • $\begingroup$ I felt the same, but then I felt silly when I found such a case, I knew a digit for sure by my own deduction, but I refused to write it down. So now I use it whenever I can, sometimes even in a longer chain that would allow 2 possibilities if not broken somewhere by a third digit. $\endgroup$
    – Florian F
    Commented Jun 3 at 20:05
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    $\begingroup$ @mgarey: I've seen CtC suggest mentally modeling a solve as a proof that a puzzle has exactly one solution (e.g., every step must be proven, with bifurcation being invalid unless one proves that exactly one route succeeds). A "full" solution of this sort of puzzle would thus require one to solve the puzzle twice: Once with anti-duplication permitted and again with it being forbidden, but with the fog removed. Mind you, this is super gross and nobody actually does it. $\endgroup$
    – Brian
    Commented Jun 3 at 21:28
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    $\begingroup$ I find it's a valid technique both in Sudoku and Kakuro: four orthogonally aligned cells with the same pair cannot be a unique solution. $\endgroup$
    – Weather Vane
    Commented Jun 3 at 21:56
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    $\begingroup$ Having spent quite some time watching CtC, I think their stance on "reasoning from uniqueness of the solution" is 1: if you are speed solving in a competition, just go for it. 2: if you are explicitly given the information that the solution is unique (like here), you can use it. 3: otherwise, it isn't a valid deduction; nothing in the basic sudoku rules says that the solution to a given puzzle must be unique. $\endgroup$
    – Bass
    Commented Jun 5 at 3:54

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