The New Sudoku Players' Forum

[Wolfgang]

But is it an enjoyable technique? ...But I suppose you can say that you never claimed the puzzle would be enjoyable...

Well, yes, i just tried to produce hard puzzles. Now i have to decide, if it is enoyable for me to tell my program to produce (hard) "human" puzzles

[Wolfgang]

As a beginning,
scrose, can you enjoy this one?

I added the numbers
4 in (1,6), 3 in (3,9), 4 in (6,2) and 8 in (6,3)
to make it manually solvable without t&e
(it would be unique without them also)

0 0 1 0 5 4 0 0 0
4 0 0 0 0 0 0 1 0
0 0 0 9 2 0 7 0 3
1 2 3 0 0 0 0 0 0
9 0 0 2 0 0 0 0 8
0 4 8 0 0 0 3 0 0
0 3 9 0 6 0 0 0 4
8 0 4 3 0 7 0 0 5
0 0 0 4 0 0 0 0 0

[scrose]

I think your new puzzle still requires some trial-and-error. I was able to fill 9 cells before "getting stuck".

Update: Using the colouring technique, I managed to eliminate a candidate 1 from r9c5, but it hasn't let me get any further.

[Hammerite]

Code: Select all

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

This one comes from another user, tso. I got it from his topic on the Suggestions board. I found it pretty difficult... although it doesn't use very advanced reasoning, it's hard to get your head around when you're used to the regular box layout. (Each row, column, and enclosed area has to contain all of the digits 1 to 9.)

[Wolfgang]

I think your new puzzle still requires some trial-and-error. I was able to fill 9 cells before "getting stuck"...

I tried it myself and i am rather sure that you can solve it without trial-and-error, though you might need some tricky combinations. Please tell me where you got stuck.

[angusj]

Please tell me where you got stuck.

Code: Select all

3.1|.54|...
4.2|.3.|51.
.8.|921|743
-----------
123|...|...
9..|2.3|..8
.48|...|3..
-----------
.39|.6.|..4
8.4|3.7|..5
...|4..|.3.


[3]     [79]    [1]     [67]    [5]     [4]     [2689]  [2689]  [269]   
[4]     [79]    [2]     [678]   [3]     [68]    [5]     [1]     [69]   
[56]    [8]     [56]    [9]     [2]     [1]     [7]     [4]     [3]     
[1]     [2]     [3]     [568]   [4789]  [5689]  [469]   [5679]  [679]   
[9]     [56]    [567]   [2]     [14]    [3]     [14]    [567]   [8]     
[567]   [4]     [8]     [156]   [179]   [569]   [3]     [25679] [12679]
[257]   [3]     [9]     [158]   [6]     [258]   [18]    [78]    [4]     
[8]     [16]    [4]     [3]     [19]    [7]     [1269]  [269]   [5]     
[2567]  [156]   [567]   [4]     [89]    [2589]  [1689]  [3]     [1679] 


[Wolfgang]

1 in box 8:

If you have a 1 in (8,5) or (9,5),
the 1s in (6,4), (5,7) and (9,9) directly follow.

But then you would have 3 1s in the rows 8 and 9,
which is not possible.

So the 1 of box 8 must be in (7,4).

You can continue then with the 1 in box 7.

[angusj]

1 in box 8:

I agree with your logic.
However, I would argue that this is (to me) still a case of trial and error - try 1 in r8c5 and low and behold it doesn't work.

[Wolfgang]

However, I would argue that this is (to me) still a case of trial and error ...

Well, this step and the next one below is clearly in the grey zone between
logically derived and using trial&error. But it is far away of the problems
you run into, if the 4 redundant numbers are not given. Then you really have
no chance than guessing.
And the title of the thread is "really hard". I would maintain that a puzzle
that is solvable with the standard techniques cannot be really hard but it
is "mechanically solvable".
So here is the next step for those who dont like such complex derivations:

If 1 is in (8,7), (8,2) becomes 6 and (8,8) is 2. But then only
(6,9) is left for both 1 and 2. So (8,2) has to be 1.

[puzzleman]

I have tried Sudoku puzzles that rated themselves as easy, medium and hard. I didn't find the "hard" at all hard; they just took a little longer. Can anyone steer me to some really hard puzzles? The ones I have looked at so far have easily fallen to the 3 or 4 step process I developeded in solving the two "easy" ones.

I would love to find something solvable but hard.

TIA,

B. King

Here is a hard puzzle containing some xwings, swordfish and nishios. Enjoy

4-----2--
9-3---1--
----14---
2----1---
-4--75---
-------3-
-5-6----4
-9------7
-1-4-86-5

[angusj]

Code: Select all

4-----2--
9-3---1--
----14---
2----1---
-4--75---
-------3-
-5-6----4
-9------7
-1-4-86-5

I like that one because it can be solved using colors (filtering on 9s) without having to resort to Nishio.

[Wolfgang]

Here is a hard puzzle containing some xwings, swordfish and nishios. Enjoy

hi, i cannot find any difficulty in this puzzle. If you see that (3,4) has to be 9 because of the 5/8-pair in (3,1) and (3,3) (the only other possibilty left would be 8 for this cell), everything is straightforward without using xwings etc.

[simes]

I don't see a 5/8 pair in (3,1) (3,3). According to my pencil marks, (3,3) has candidates 5, 6 and 8. Or were you able to eliminate the 6 somehow?

[Wolfgang]

I don't see a 5/8 pair in (3,1) (3,3). According to my pencil marks, (3,3) has candidates 5, 6 and 8. Or were you able to eliminate the 6 somehow?

Ah yes, excuse me, i oversaw that my program eliminated the 6 in (3,3) before which was not trivial at all.

[scrose]

I like that one because it can be solved using colors (filtering on 9s) without having to resort to Nishio.

...everything is straightforward without using xwings etc.

I agree with Wolfgang's opinion that the x-wing technique does not necessarily need to be applied. By applying angusj's recommendation of colours on the 9's, you can bypass the use of the x-wing technique; by eliminating one candidate 9, you will be able to place a 9 in r3c4 in two moves.