## Tough puzzle

Post the puzzle or solving technique that's causing you trouble and someone will help

### Tough puzzle

any suggestion??

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

Kent

Posts: 98
Joined: 28 February 2006

This is the third posting of the same puzzle, you've posted Here and Here, there is no need for this.

Also, there is a candidate grid in the last link, your first post.

MCC
MCC

Posts: 1275
Joined: 08 June 2005

MCC

there is a candidate grid in the last link

What do u mean candidate grid???

This is a totally new puzzle.I am sorry I made a mistake by posting same puzzle on different thread.
Kent

Posts: 98
Joined: 28 February 2006

The candidate grid:

Code: Select all
5      1      278    |  2678   678    3      |  9      678    4
279    4      278    |  2678   6789   5      |  268    3      1
6      279    3      |  1      4      2789   |  5      78     278
----------------------+-----------------------+-----------------------
8      3      1      |  2567   679    2679   |  4      569    69
24     25     9      |  3      1      2468   |  7      568    68
47     57     6      |  578    789    4789   |  1      2      3
----------------------+-----------------------+-----------------------
3      679    4      |  678    2      1      |  68     6789   5
1      8      27     |  9      5      67     |  3      4      267
279    2679   5      |  4      3      678    |  268    1      26789

Without it it's hard to tell which eliminations you have done before getting stuck. There are several box/line interactions (locked candidates) here, but we can't say which one you have found yet without knowing your candidates.

This is a pretty hard puzzle, by the way. Your next move, after several of the above-mentioned box/line eliminations, could be to locate a finned X-Wing in 6s.

It gets a bit tougher after that, though.

Vidar
vidarino

Posts: 295
Joined: 02 January 2006

Code: Select all
5      1      278    |  2678   678    3      |  9      678    4
279    4      278    |  2678   6789   5      |  268    3      1
6      279    3      |  1      4      2789   |  5      78     278
----------------------+-----------------------+-----------------------
8      3      1      |  2567   67    267     |  4      569    69
24     25     9      |  3      1      46     |  7      568    68
47     57     6      |  578    789    489   |  1      2      3
----------------------+-----------------------+-----------------------
3      679    4      |  678    2      1      |  68     6789   5
1      8      27     |  9      5      67     |  3      4      267
279    2679   5      |  4      3      678    |  268    1      26789

I'm sorry.This s the candidate grid i'm at.I'm stuck here
Kent

Posts: 98
Joined: 28 February 2006

512|873|964
748|695|231
693|142|578
---------------
831|267|459
259|314|786
476|589|123
----------------
364|721|895
187|956|342
925|438|617
Guest

### Tough Puzzle

Hi canigia,
I'm sure you think you are helping by posting the solution but the forum is for "helping to solve" the puzzle. Simply posting the solution does nothing to teach anyone how to solve it. There are ample solver programs available which can provide an immediate solution to a puzzle but few of us, if any, can get excited doing that. If you look back through the forum's posts you'll see how solving techniques are posted and you are of course welcome to do that but please refrain from posting future solutions.
Cec
Cec

Posts: 1039
Joined: 16 June 2005

After Locked candidate 2 in box 4, 7 in box 4, 8 in box 6 and 9 in box 6, you should get here:

Code: Select all
+----------------+------------------+------------------+
| 5    1     278 | 2678  678   3    | 9    678   4     |
| 279  4     278 | 2678  6789  5    | 268  3     1     |
| 6    279   3   | 1     4     2789 | 5    78    278   |
+----------------+------------------+------------------+
| 8    3     1   | 2567  67    267  | 4    569   69    |
| 24   25    9   | 3     1     46   | 7    568   68    |
| 47   57    6   | 58    89    489  | 1    2     3     |
+----------------+------------------+------------------+
| 3    679   4   | 678   2     1    | 68   6789  5     |
| 1    8     27  | 9     5     67   | 3    4     267   |
| 279  2679  5   | 4     3     678  | 268  1     26789 |
+----------------+------------------+------------------+

Where I join you in Stuckville.

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005

Mac, you're stuck here too??
Kent

Posts: 98
Joined: 28 February 2006

Code: Select all
5      1      278    |  2678   678    3      |  9      678    4
279    4      278    |  2678   6789   5      |  268    3      1
6      279    3      |  1      4      2789   |  5      78     278
----------------------+-----------------------+-----------------------
8      3      1      |  2567   67     267    |  4      569   -69
24     25     9      |  3      1     *46     |  7     #568   *68
47     57     6      |  58     89     489    |  1      2      3
----------------------+-----------------------+-----------------------
3      679    4      |  678    2      1      |  68     6789   5
1      8      27     |  9      5     *67     |  3      4     *267
279    2679   5      |  4      3      678    |  268    1      26789

A good, old Finned X-Wing in R58C69 + fin in R5C8, eliminates the 6 in R4C9.

As mentioned, this is a pretty tough one. It gets worse...
vidarino

Posts: 295
Joined: 02 January 2006

Thanks vidar.Didnt really see that one.Just curious how long did u take to see that one??? Do u try to look out for other methods like colouring, forced chains before looking for x-wing?
Kent

Posts: 98
Joined: 28 February 2006

I cheated. I used my solver program this time. ;)

But normally, when solving moderately tough puzzles I filter digits one by one, looking for X-Wings, Swordfishes and doing basic coloring in my head (a.k.a. looking for X-Cycles - which sometimes leads to loops that double as finned fish, even). If that fails, I usually move on to bivalue / XY-Chains, and if that fails, more complex nice loops. (I'm not too great at figuring those out yet, though.)

One thing I have absolutely NO mastery in yet is the detection of Almost Locked Sets (which this puzzle will require, as far as I (or my solver) can tell).
vidarino

Posts: 295
Joined: 02 January 2006

### A Possible Solution

Code: Select all
*--------------------------------------------------------------------*
| 5      1      278    | 2678   678    3      | 9      678    4      |
| 279    4      278    | 2678   6789   5      | 268    3      1      |
| 6      279    3      | 1      4      2789   | 5      78     278    |
|----------------------+----------------------+----------------------|
| 8      3      1      | 2567   67     267    | 4      569    69     |
| 24     25     9      | 3      1      46     | 7      568    68     |
| 47     57     6      | 58     89     489    | 1      2      3      |
|----------------------+----------------------+----------------------|
| 3      679    4      | 678    2      1      | 68     6789   5      |
| 1      8      27     | 9      5      67     | 3      4      267    |
| 279    2679   5      | 4      3      678    | 268    1      26789  |
*--------------------------------------------------------------------*

-7-[r7c4|r7c7]-6-[r7c2]=6=[r9c2]-{Nice Loop: [r5c9]=8=[r5c8]=5=[r4c8]-5-[r4c4]=5=[r6c4]-5-[r6c2]-7-[r7c2]=7=[r7c8]=9=[r9c9]-9-[r4c9]-6-[r5c8|r5c9]}-6-[r5c8|r5c9]-5-[r5c2]=5=[r6c2]-5-[r6c4]-8-[r6c5]-9-[r2c5]=9=[r2c1]-9-[r9c1]=9=[r9c9]-9-[r4c9]-6-[r8c9]=6=[r8c6]-6-[r5c6]-4-[r5c1]-2-[r5c2]

which means that, if r7c4 is not "7" then r5c2 turns out to be an empty cell - a contradiction. So, r7c4=7 and that solve the puzzle.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

After Vidars finned x-wing you come here

Code: Select all
*-----------------------------------------------------------*
| 5     1     278   | 2678  678   3     | 9     678   4     |
| 279   4     78    | 678   6789  5     | 268   3     1     |
| 6     279   3     | 1     4     2789  | 5     78    28    |
|-------------------+-------------------+-------------------|
| 8     3     1     | 2567  67    267   | 4     56    9     |
| 24    25    9     | 3     1     46    | 7     568   68    |
| 47    57    6     | 58    89    489   | 1     2     3     |
|-------------------+-------------------+-------------------|
| 3     67    4     | 678   2     1     | 68    9     5     |
| 1     8     27    | 9     5     67    | 3     4     267   |
| 279   2679  5     | 4     3     678   | 268   1     2678  |
*-----------------------------------------------------------*

and can use this loop:
r3c6(=2=r4c6=7)-9-r3c2=9=r2c1-9-r9c1=9=r9c2=6=r7c2-6-r7c8-8-r7c4-7-r89c6
=>r6c6=9
That means, if r3c6=9, then
1. r4c6=2 <> 7
2. r2c1=9 and r9c2=9, r7c2=6 (col 2), r7c7=8, r7c4=7 and r89c6<>7
Then there is no 7 left in column 6.
ravel

Posts: 998
Joined: 21 February 2006

I tried 8 in r6c5, which led to a solution easily.

So I tried 9. That was more fun, with several interesting locked candidates. But I eventually got to here

Code: Select all
+-------------+--------------+-----------+
| 5   1   278 | 27   78   3  | 9   6  4  |
| 9   4   78  | 67   678  5  | 2   3  1  |
| 6   2   3   | 1    4    9  | 5   8  7  |
+-------------+--------------+-----------+
| 8   3   1   | 567  67   2  | 4   9  69 |
| 24  2   9   | 3    1    46 | 7   5  68 |
| 47  57  6   | 58   9    48 | 1   2  3  |
+-------------+--------------+-----------+
| 3   9   4   | 68   2    1  | 68  7  5  |
| 1   8   27  | 9    5    67 | 3   4  26 |
| 27  6   5   | 4    3    78 | 8   1  29 |
+-------------+--------------+-----------+

with 2 candidates 2 in column 2. That is two [stet] funny!

Anyway, thus there is only one solution.

I post this mainly to ask if there is a good way to distinguish between cells with a single candidate and cells that have been solved.

Maybe
Code: Select all
+-------------+
| 5  1    278 |
| 9  4    78  |
| 6  {2}  3   |
+-------------+

I would hate to put brackets around all candidate lists as it scrolls off the right of the page more than ever when there are many cells with multiple candidates.

Mac
QBasicMac

Posts: 441
Joined: 13 July 2005