The New Sudoku Players' Forum

[Carcul]

Consider the following grid:

Code: Select all

 *----------------------------------------------------*
 | 1     24    3  | 48    5     6  | 279   278   289  |
 | 5     9     8  | 7     3     2  | 6     4     1    |
 | 7     246   46 | 1     9     48 | 3     5     28   |
 |----------------+----------------+------------------|
 | 4     17    9  | 6     8     3  | 27    127   5    |
 | 8     3     67 | 2     1     5  | 47    9     46   |
 | 2     16    5  | 9     4     7  | 8     16    3    |
 |----------------+----------------+------------------|
 | 6     48    14 | 3     7     19 | 5     28    289  |
 | 9     5     2  | 48    6     48 | 1     3     7    |
 | 3     78    17 | 5     2     19 | 49    68    4689 |
 *----------------------------------------------------*


Solve it in one step by finding first what is wrong with it.

Carcul

[Mike Barker]

The correct grid is:

Code: Select all

+--------------+------------+-----------------+
| 1   24    3  | 48  5   6  | 279  278   289  |
| 5    9    8  |  7  3   2  |   6    4     1  |
| 7  246   46  |  1  9  48  |   3    5    28  |
+--------------+------------+-----------------+
| 4   17    9  |  6  8   3  |  27  127     5  |
| 8    3   67  |  2  1   5  |  47    9    46  |
| 2   16    5  |  9  4   7  |   8   16     3  |
+--------------+------------+-----------------+
| 6   48*  14  |  3  7  19- |   5   28* 2489* |
| 9    5    2  | 48  6  48  |   1    3     7  |
| 3  478* 147  |  5  2  19- |  49   68* 4689* |
+--------------+------------+-----------------+

The son of Sho thought he saw a UR on 4,8 in r79c29. Because of the strong link on 8 in column 2, the bivalue (I could get use to calling it a bivalve - fits in with all things fishy) in r9c8 and the ALS in r13c9, if r7c9=8 then a deadly pattern emerges. Our unfortunate fellow then eliminated the 4 instead of the 8! With the resulting locked candidates he then eliminated the 4's from r9c23 which gives the PMs as shown. Realizing the puzzle is no longer valid it is clear that r7c9=4 and joy returns to Mudville.

[ronk]

Our unfortunate fellow then eliminated the 4 instead of the 8!
(...)
Realizing the puzzle is no longer valid it is clear that r7c9=4 and joy returns to Mudville.

Proving that r7c9<>8 is not the same as proving r7c9=4. How did you make that leap?

[Mike Barker]

You are right that removing 8 from r7c9 doesn't solve the puzzle, but we know removing 4 leads to an invalid puzzle, therefore, r7c9 must be equal to 4. I think Gurth calls this a GET.

[daj95376]

Code: Select all

# PMs before incorrect elimination
 *-----------------------------------------------------------*
 | 1     24*   3     | 48*   5     6     | 279   278   289   |
 | 5     9     8     | 7     3     2     | 6     4     1     |
 | 7     246*  46*   | 1     9     48*   | 3     5     28    |
 |-------------------+-------------------+-------------------|
 | 4     17    9     | 6     8     3     | 27    127   5     |
 | 8     3     67    | 2     1     5     | 47    9     46    |
 | 2     16    5     | 9     4     7     | 8     16    3     |
 |-------------------+-------------------+-------------------|
 | 6     48*   14*   | 3     7     19    | 5     28    2489- |
 | 9     5     2     | 48*   6     48*   | 1     3     7     |
 | 3     478-  147-  | 5     2     19    | 49    68    4689  |
 *-----------------------------------------------------------*


Either there is a Jellyfish in [r1378c2346] for <4> or else [r7c9]=4. For some reason, the Jellyfish was selected as true and [r7c9]<>4, [r9c23]<>4 resulted. Correctly selecting [r7c9]=4 results in a cascade of singles that solve the puzzle.

[Carcul]

... but we know removing 4 leads to an invalid puzzle

And how did you find that? I hope it was not with the aid of your solver... because the purpose of this (and all others) exercises its to think by yourself. Anyway, you missed completely the purpose of the exercise, as Daj.
If you (or anybody else) want to use a computer, its ok by me, but then please don't post the conclusions of the computer.

The error that you are making here is precisely the same that was done in The Riddle of Sho: starting by find what candidate was incorrectely eliminated and then thinking what was done wrong.
Please read carefully the "riddle". I have written "by finding first what is wrong with it" and not "by finding first what candidate(s) was(were) incorrectly eliminated". Note the difference?

Anyway:

The son of Sho thought he saw a UR on 4,8 in r79c29. Because of the strong link on 8 in column 2, the bivalue (I could get use to calling it a bivalve - fits in with all things fishy) in r9c8 and the ALS in r13c9, if r7c9=8 then a deadly pattern emerges. Our unfortunate fellow then eliminated the 4 instead of the 8!

Don't be ridiculous. How could someone do that?
This exercise don't have anything to do with someone that did some error. The purpose is not to imaginate an incredible error that was made by a virtual entitie. You have a grid in front of your eyes. Use them, together with your brain, and a pencil if you like. Now, find what is wrong with the grid.

And btw, Sho doesn't have any son.

Carcul

[Del]

r7c3 is given as 14 but there is only one 1 shown in row 7, therefore r7c3=1 and r9c3=7 etc.
Is this the answer?

Regards,
Del

Sorry , I missed the other one at r7c6.

[Ruud]

You have a grid in front of your eyes. Use them, together with your brain, and a pencil if you like. Now, find what is wrong with the grid.

When I color the large B/B cluster, this is the result:



Both colors cause a conflict in row 9:
2 violet digits 9
2 green digits 8

Therefore the grid is invalid.

Ruud

[Carcul]

Very good Ruud. That is the type of "wrongness": two incompatible loops. Now the true purpose of the exercise is to find the correct TILs and use them to infere "what went wrong" (although you can also use your loops, but I think it would be somewhat harder). Hint: you pratically don't need to make any marks in the grid (colors, letters, lines, circles) in order to find them.

Learn to look carefully to a (pencilmarked) grid before starting to overcrowd it with additional symbols. See first, think after, and write last.

Good luck, Carcul

[daj95376]

[Edited] Deleted angry comments.

[Carcul]

Daj, obviously if I didn't post the original puzzle is because it is not needed (that was my "error" in The Riddle of Sho). If I were to post it, then the answer could be reached very easily. If I didn't say that all single-valued cells are correct, is because that information is also not needed.

...that any of us were foolish enough to attempt your exercise without first demanding that you post the original puzzle.

At least your poorly-worded exercise taught us that!!!

I think I am the foolish one, by giving additional clues. Suppose you are doing a final exam on Chemistry and you don't know how to solve a question. Would you expect your teacher to give you clues by saying him "Hey, this question is poorly-worded!"? I don't think so. Why? Well, I think I don't need to answer that.

Carcul

[ronk]

Both colors cause a conflict in row 9:
2 violet digits 9
2 green digits 8

Therefore the grid is invalid.

That is the type of "wrongness": two incompatible loops.

Good find, Ruud. Only one loop -- either one -- is sufficient to show the grid to be invalid, however. That said, both loops are likely required to deduce the error in the grid.

[ravel]

That is the type of "wrongness": two incompatible loops.

Code: Select all

 *----------------------------------------------------*
 | 1     24    3  | 48    5     6  | 279   278   289  |
 | 5     9     8  | 7     3     2  | 6     4     1    |
 | 7     246   46 | 1     9     48 | 3     5     28   |
 |----------------+----------------+------------------|
 | 4     17    9  | 6     8     3  | 27    127   5    |
 | 8     3     67 | 2     1     5  | 47    9     46   |
 | 2     16    5  | 9     4     7  | 8     16    3    |
 |----------------+----------------+------------------|
 | 6     48    14 | 3     7     19 | 5     28    289  |
 | 9     5     2  | 48    6     48 | 1     3     7    |
 | 3     78    17 | 5     2     19 | 49    68    4689 |
 *----------------------------------------------------*


Here are two (ignoring a hidden pair and an xy-wing):
r5c3=6 => r4c2=7 => r9c2=8 => r9c8=6 => r5c9=6
r5c3=7 => r5c7=4 => r9c7=9 => r9c6=1 => r9c3=7

[udosuk]

Code: Select all

 *----------------------------------------------------*
 | 1     24    3  | 48    5     6  | 279   278   289  |
 | 5     9     8  | 7     3     2  | 6     4     1    |
 | 7     246   46 | 1     9     48 | 3     5     28   |
 |----------------+----------------+------------------|
 | 4     17    9  | 6     8     3  | 27    127   5    |
 | 8     3     67 | 2     1     5  | 47    9     46   |
 | 2     16    5  | 9     4     7  | 8     16    3    |
 |----------------+----------------+------------------|
 | 6     48    14 | 3     7     19 | 5     28   #289  |
 | 9     5     2  | 48    6     48 | 1     3     7    |
 | 3     78    17 | 5     2     19 |*49    68   *4689 |
 *----------------------------------------------------*


One approach is noticing that there are only 2 possible cells for 4s in box 9 - r9c7 & r9c9.

r9c9=4 -> r5c9=6 -> r5c3=7 -> r9c3=1 -> r9c6=9 -> r9c7=4
-> Two 4s on r9!

r9c7=4 -> r5c9=4 -> r6c8=6 -> r6c2=1 -> r4c2=7 -> r9c2=8 -> r9c8=6
-> Two 6s on c8!

Therefore the grid is invalid.

Assuming all single-candidate cells are correct, the 4 must be elsewhere in box 9... The only possible cell for it is in r7c9. Assuming r7c9=4, the grid can be solved via singles.

I don't know if this approach is valid or not because I'm not sure the assumption that "all single-candidate cells are correct" is valid here...

If I didn't say that all single-valued cells are correct, is because that information is also not needed.

If we don't know the original puzzle and can't be sure whether "all single-valued cells are correct", then there is really nothing we're logically sure... The "correct solution" could well be this grid:

Code: Select all

 1 2 3 | 4 5 6 | 7 8 9
 4 5 6 | 7 8 9 | 1 2 3
 7 8 9 | 1 2 3 | 4 5 6
-------+-------+-------
 2 3 1 | 5 6 4 | 8 9 7
 5 6 4 | 8 9 7 | 2 3 1
 8 9 7 | 2 3 1 | 5 6 4
-------+-------+-------
 3 1 2 | 6 4 5 | 9 7 8
 6 4 5 | 9 7 8 | 3 1 2
 9 7 8 | 3 1 2 | 6 4 5