The New Sudoku Players' Forum

[DukeJP2010]

Page 17 of Sudoku Genius by Tom Sheldon.

This is what I have so far:

Code: Select all

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

I have solved it using guessing, but the front of the book says that this puzzle does not require guessing.

Any help?

[udosuk]

No guessing required. Here are some hints:

Focus on column 4. The digits 1,2,8 can only be located in 3 cells (r569c4). Therefore these 3 cells must only contain these 3 digits, and no other digit. (This is called a hidden triple.)

Now focus on block 5. There is only 1 possible cell which can hold a 9 now (r5c6). (This is called a hidden single.)

Now focus on row 6. There is only 1 possible cell which can hold a 9 now (r6c3). (Another hidden single.)

The rest of the puzzle can be solved easily with more hidden singles (or naked singles - cells with only 1 possible digit left).

BTW it would be better if you can post the puzzle in its original form (i.e. the initial clues only).

[DukeJP2010]

R6C4 can be an 8? what about the 8 in R6C8?

-Jason

P.S. i looked in the back, and every number I have so far is correct. I would just like to know the logic to continue forward.

[re'born]

R6C4 can be an 8? what about the 8 in R6C8?

Jason,
Udosuk meant that the numbers 1,2 and 8 can appear nowhere else but r569c4, not that they have to appear in all three. In this case, 1 can appear in all three, 2 can only appear in r56c9 and 8 can only appear in r59c4. In total, you have three numbers that appear in a total of at most three cells in a column. Therefore, those three cells must contain (in some order) precisely those three numbers, namely, 1,2 and 8.

[udosuk]

P.S. i looked in the back, and every number I have so far is correct. I would just like to know the logic to continue forward.

Even if you haven't made a mistake, it might be nice to post the original puzzle just so that others can see the difficulty of the whole puzzle.

BTW thanks re'born for explaining for me.

[DukeJP2010]

Thank you for your help. I have solved the puzzle.

I guess another way of looking at it is that there are 6 unknowns in c4, and 3 of them CAN'T be a 1,2, or 8, so the other three HAVE to be a 1, 2, or an 8.

Thanks again!

-Jason

[udosuk]

I guess another way of looking at it is that there are 6 unknowns in c4, and 3 of them CAN'T be a 1,2, or 8, so the other three HAVE to be a 1, 2, or an 8.

Yes, what you described is called a naked triple. If you have gone to the trouble to listing all the candidates (pencilmarks) for each cell it will be very obvious. I was assuming you were doing it without pencilmarks so told you about the hidden triple instead.

Some links:

http://www.sudopedia.org/wiki/Hidden_Triple

http://www.sudopedia.org/wiki/Naked_Triple

[DukeJP2010]

Thank you for you help. I'm stuck on another puzzle in the same book (I have done several since.) This one from page 71.

The book is divided into 9 "circles of Sudoku hell."

What I previously posted was a "Circle 1" puzzle. This one is a Circle 3.

Start:

Code: Select all

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


And here is how far I've got.

Code: Select all

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

I do pencil in every possible number, I guess I just missed it on that one.

Thanks in advance for your help!

-Jason

[udosuk]

http://www.sudopedia.org/wiki/Hidden_Pair

http://www.sudopedia.org/wiki/Naked_Quad

Focus on column 9.

[DukeJP2010]

Thank you, I solved it. All I needed was to see that naked quad.

Any tips on how to spot these?

[re'born]

Thank you, I solved it. All I needed was to see that naked quad.

Any tips on how to spot these?

Flippant answer: Look for them.

What I mean by this is that for most people, naked quads will not just jump off the page at you. However, if you've put in pencilmarks and you look explicitly for them, it isn't so bad. Here are a few things to help you on your way.

1. To do an exhaustive search, look in each row, column and block.
2. To do a somewhat smarter search, look only at the rows, columns and blocks that have at least 5 unsolved cells (so in your puzzle, this already eliminates rows 1,3,4,6,8; columns 3,5,6,8; blocks 1,2,3,6 from having useful naked quads).
3. If a row, column or block has exactly 5 unsolved cells and it has a naked quad, then it must also have a hidden single. If you've already ruled out hidden singles in the grid, then you can rule out any row, column or block with exactly 5 unsolved cells. In your puzzle, this eliminates from contention rows 2,9; column 2; blocks 4,5,7,9.

Using 2&3, one only needs to check for naked quads (assuming you've already checked for hidden singles)
rows: 5,7 (there aren't any)
columns: 1,4,7,9 (there is one in column 9)
block: 8 (there aren't any)

4. No cell with more than 4 candidates can be a part of a naked quad.
5. If you aren't using pencilmarks, it is usually easier to spot hidden singles, hidden pairs, hidden triples and hidden quads. If you spot all of these first, the only time you'll miss a naked quad is if it occurs in a row, column or block with no solved cells.

I hope these help.

[ab]

2. To do a somewhat smarter search, look only at the rows, columns and blocks that have at least 5 unsolved cells (so in your puzzle, this already eliminates rows 1,3,4,6,8; columns 3,5,6,8; blocks 1,2,3,6 from having useful naked quads).

You only have to look in a row/column/box with 8 or 9 unsolved cells. Any with less could be solved with a triple, pair or single.