The New Sudoku Players' Forum

[Norten29]

[tso]

Does anyone know a better, or more extensive rule for hidden pairs?

The description Angus gives is correct. Perhaps some examples will help.

Here are 9 cells in a row:

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[12345][12567][<>12]|[<>12][<>12][<>12]|[<>12][<>12][<>12]

The first two cells have 5 candidates including a '1' and a '2'. The next 7 cells can have anything at all other than a '1' or a '2' (I'm using '<>' to mean 'not'). So there are TWO candidates that only appear in TWO cells. The only possible results are that either the first cell is 1 and the second is 2 OR the first cell is 2 and the second is 1. Either way, no other candidate can exist in the first two cells, leaving you with:

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[12---][12---][<>12]|[<>12][<>12][<>12]|[<>12][<>12][<>12]

Hidden triples take it a step further:

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[12345][12356][12356]|[<>123], etc.
[12345][12356][12-56]|[<>123], etc.
[12345][1-356][12-56]|[<>123], etc.
[-2345][1-356][12-56]|[<>123], etc.

In each of these four cases, the digits 1, 2 and 3 appear ONLY in the first three cells -- so the first three cells are full -- all other candidates are eliminated:

[EDIT: type corrected]

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[123--][123--][123--]|[<>123], etc.
[123--][123--][12---]|[<>123], etc.
[123--][1-3--][12---]|[<>123], etc.
[-23--][1-3--][12---]|[<>123], etc.

THREE candidates appearing in only THREE cells.

[ronk]

One of the features of Simple Sudoku is that it flags or reports whenever an invalid move is made. The reason I say the rule for hidden pairs is insufficient is that often when I follow it explicitly, my move is declared invalid.

A specific case might be in order. When you get an "invalid move", you can copy and paste the candidate grid from Simple Sudoku to this thread ... and describe the move you're trying to make.

Someone can then explain why the move is invalid.

[Cec]

In each of these four cases, the digits 1, 2 and 3 appear ONLY in the first three cells -- so the first three cells are full -- all other candidates are eliminated:

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[123--][123--][12356]|[<>123], etc.
[123--][123--][12---]|[<>123], etc.
[123--][1-3--][12---]|[<>123], etc.
[-23--][1-3--][12---]|[<>123], etc.

THREE candidates appearing in only THREE cells.

Unless I'm mistaken shouldn't the third cell in the top row read [123--]
Cec

[QBasicMac]

The reason I say the rule for hidden pairs is insufficient is that often when I follow it explicitly, my move is declared invalid. Does anyone know a better, or more extensive rule for hidden pairs?

The following pencilmarks show a hidden pair in r8c7 r9c7:

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+-------------------+-----------------+--------------+
| 2      149   59   | 149   159   3   | 6     7   8  |
| 357    134   357  | 6     158   248 | 13    24  9  |
| 6      1349  8    | 149   7     249 | 13    24  5  |
+-------------------+-----------------+--------------+
| 349    5     39   | 349   6     1   | 7     8   2  |
| 489    7     6    | 489   2     489 | 5     3   1  |
| 38     2     1    | 5     38    7   | 4     9   6  |
+-------------------+-----------------+--------------+
| 35789  389   3579 | 1389  4     6   | 2     15  37 |
| 1      389   2    | 7     389   5   | 389   6   4  |
| 35789  6     4    | 2     1389  89  | 1389  15  37 |
+-------------------+-----------------+--------------+


As you can see, every candidate 8 and 9 in box 9 fall into those two cells. Therefore 8 and 9 must be placed there in some order. That means no other candidate is valid in those two cells.

You can erase 3 from r8c7
You can erase 1 and 3 from r9c7.

There is nothing else you can erase.

If that is what you have been doing, then you have probably simply made a clerical mistake. No software (I hope) would reject those three erasures.

If these general replies don't help, you really need to do what ronk said: Solve a puzzle up to the invalid erasure in a hidden pair and then post a grid similar to mine above and tell us which cell you tried to erase what from.

Mac