The New Sudoku Players' Forum

[AnotherLife]

Hi everyone,
I faced this puzzle on a website, and it was meant to be solved without automatic detection of the candidates and with no possibility to highlight the digits and draw anything.
1. How would you solve it?
2. Do you think it is hard and tedious?

Code: Select all

4....25....2.3.6.......9..7...15.4.......6.1..9......3..3.1...2.65.........7.3...

[SteveG48]

Interesting puzzle. Basically, you are asking for a pencil and paper solution. Setting it up, completing the grid, and doing the basics is no more (or less) tedious than that exercise usually is.

After that, you hit a brick wall (unless you're a lot better than me, which would not be unusual). Convincing yourself of that is always tedious.

The interesting part is that if you elect to proceed by trial and error, almost all of the cells with just two candidates will get you to a solution.

[AnotherLife]

Hi Steve,
Firstly, I think it is tedious to fill up to six candidates in the cells (there are only five singles at the beginning). If you make a mistake, nobody will correct you. Secondly, I am not quite sure what you mean by hitting a brick wall. I always seek logical means to solve puzzles and I never proceed by trial and error. Maybe I am a masochist. I just wanted to see how different people would choose to solve this puzzle under the above conditions.

[SteveG48]

Hi, Bogdan. When I say hitting a brick wall, I mean that I've gotten to a place in the puzzle where none of the logical techniques that I'm likely to use when solving with pencil and paper are going to work. That seems to be the case here.

I never use trial and error either. I just find it interesting that doing so would be effective here.

[eleven]

2: yes

Code: Select all

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

After a long and tedious search and with good memory (and Steve's useful hint, that 2 candidates cells would solve it - at least 7 of the bilocal digits are "running" with singles too), you could see, that 6r6c8 implies 6 in r7c4,r1c3 and r4c1 -> 3r4c2, 2r4c8, and 9r4c9. This leaves only one cell for 3 and 9 in row 1 => contradiction.

Code: Select all

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

But goodness knows, what i missed ...

[AnotherLife]

I also got stuck at some point and I thought that maybe I was blind and couldn't see something obvious. I have said in several posts that we need a good rating system to estimate puzzles in a right way. In this case, the conventional systems SER and SKFR give the informative value 7.2, and it means that the puzzle cannot be solved by standard patterns, so we need to construct chains. Knowing that, I managed to get a long solution by ALS-chains in several sessions. It was hard because I could neither highlight the digits nor draw the lines. I don't know if such a way was meant by those who offered me this puzzle. Eleven, your way is unusual for me.

[Cenoman]

An off-topic comment on this puzzle (since it is the result of tool use...)

The puzzle has one solution (at least one) with four chains using only conjugates (bivalues and bilocations), no group, no ALS.

Code: Select all

 +-------------------------+----------------------+--------------------------+
 |  4       138    F1689   | a68     7      2     |  5       389    A1-89    |
 |  5789    578     2      |  458    3      1     |  6       489     489     |
 |  13568   1358    168    |  4568   468    9     | B1238    2348    7       |
 +-------------------------+----------------------+--------------------------+
 |  2368    238    i678    |  1      5     h78    |  4       26789   689     |
 |  258    k248-5 Dj478    |  3      9      6     | C278     1      e58      |
 |  156     9       16     |  248    248   g478   | f78     d56      3       |
 +-------------------------+----------------------+--------------------------+
 |  789     478     3      | b4689   1      5     |  789    c4678    2       |
 |  12789   6       5      |  2489   248    48    |  13789   3478    148     |
 |  1289    1248   E1489   |  7      2468   3     |  189     4568    14568   |
 +-------------------------+----------------------+--------------------------+

1. (8=6)r1c4 - r7c4 = r7c8 - (6=5)r6c8 - (5=8)r5c9 => -8 r1c9 (tags: a to e)
2. (5=8)r5c9 - (8=7)r6c7 - r6c6 = r4c6 - r4c3 = (7-4)r5c3 = (4)r5c2 => -5 r5c2 (sequencing tags: e to k)
3. (1)r1c9 = (1-2)r3c7 = (2-7)r5c7 = (7-4)r5c3 = (4-9)r9c3 = (9)r1c3 => -9 r1c9 (tags: A to F); basics, 3 placements

Code: Select all

 +-----------------------+---------------------+-----------------------+
 |  4      38     689    |  68     7     2     |  5     389     1      |
 | a78-9  b578    2      |  458    3     1     |  6     489     489    |
 |  1368  c1358   168    |  4568   468   9     | h238   2348    7      |
 +-----------------------+---------------------+-----------------------+
 |  2368   238    678    |  1      5     78    |  4     26789   689    |
 |  258    248   j478    |  3      9     6     | i278   1       58     |
 |  156    9      16     |  2      48    478   |  78    56      3      |
 +-----------------------+---------------------+-----------------------+
 | l789    478    3      |  468    1     5     |  789   4678    2      |
 |  17     6      5      |  9      2     48    | g137   37      48     |
 |  1289  d1248  k1489   |  7      468   3     | f189   4568    4568   |
 +-----------------------+---------------------+-----------------------+

4. (7)r2c1 = (7-5)r2c2 = (5-1)r3c2 = r9c2 - r9c7 = (1-3)r8c7 = (3-2)r3c7 = (2-7)r5c7 = (7-4)r5c3 = (4-9)r9c3 = (9)r1c3 => -9 r2c1; ste

I see no technique in there, justifying a rating above the SER 7.2

Hidden Text: Show

Of course, I'd write such a solution in a more condensed way (using ALSs and AHSs) :
1. (8=6)r1c4 - r7c4 = r7c8 - (6=58)b6p68 => -8 r1c9
2. (5=87)b6p67 - r6c6 = r4c6 - r4c3 = (74)r5c23 => -5 r5c2
3. (1)r1c9 = (12-7)r35c7 = (74-9)r59c3 = (9)r1c3 => -9 r1c9; basics & 3 placements
4. (7)r2c1 = (751)r239c2 - (1=897)r679c7 - r5c7 = (749)r159c3 => -9 r2c1; ste

[AnotherLife]

The puzzle has one solution (at least one) with four chains using only conjugates (bivalues and bilocations), no group, no ALS...
...
I see no technique in there, justifying a rating above the SER 7.2

Hi Cenoman,
I said that SER 7.2 is informative here. It tells us that the puzzle needs 'forcing chains', and in more familiar terms these chains are AICs with no group- or ALS-nodes, so your solution just confirms this fact. Do you wonder why I started to apply ALS technique? Just for the hell of it. I know that it is often useful to start a chain from an ALS of 4-5 elements. For example, I gained two singles after my first step.

Code: Select all

.----------------------.-------------------.----------------------.
| 4      138    1689   | 68      7     2   | 5       389    189   |
| 5789   578    2      | 458     3     1   | 6       489    489   |
| 13568  1358   168    | 4568    468   9   | 1238    2348   7     |
:----------------------+-------------------+----------------------:
| 2368   238    678    | 1       5     78  | 4       26789  689   |
| 258    b2458  c478   | 3       9     6   | d278    1      f58   |
| 156    9      16     | 248     248   478 | e78     g56    3     |
:----------------------+-------------------+----------------------:
| a789   a478   3      | i468-9  1     5   | a789    h4678  2     |
| 12789  6      5      | 2489    248   48  | 13789   3478   148   |
| 1289   1248   1489   | 7       2468  3   | 189     4568   14568 |
'----------------------'-------------------'----------------------'

(9=784)r7c127 - r5c2 = (4-7)r5c3 = r5c7 - (7=8)r6c7 - (8=5)r5c9 - (5=6)r6c8 - r7c8 = r7c4 => -9 r7c4, 2 singles

Finally I got a long solution but later I optimized it and reduced the number of steps to three.