The New Sudoku Players' Forum

by **evert** » Thu Dec 11, 2008 1:12 pm

I tried some programming on this.

The source code so far can be found here.

My solver could solve djape's 9x9 sample puzzle on his own site.

Here's another puzzle:

Code: Select all: 00;22;20;00;00;00;00;80;00 00;00;00;00;00;00;73;00;00 00;00;00;69;00;00;00;00;77 35;00;66;00;64;05;00;00;00 00;00;27;00;00;00;00;00;00 00;39;00;03;00;00;00;00;58 00;40;00;02;30;00;00;00;12 00;43;00;00;00;00;00;00;00 00;00;00;00;47;00;10;00;52

Would anybody like to try if the puzzle is OK?

by **udosuk** » Sat Dec 13, 2008 1:11 am

evert wrote:Here's another puzzle:
Code: Select all
.. 22 20 .. .. .. .. 80 .. .. .. .. .. .. .. 73 .. .. .. .. .. 69 .. .. .. .. 77 35 .. 66 .. 64 05 .. .. .. .. .. 27 .. .. .. .. .. .. .. 39 .. 03 .. .. .. .. 58 .. 40 .. 02 30 .. .. .. 12 .. 43 .. .. .. .. .. .. .. .. .. .. .. 47 .. 10 .. 52
Would anybody like to try if the puzzle is OK?

Yep, that's a very nice Hidato/Hidoku puzzle. I'm quite certain it has a unique solution as the following:

Highlight below to see what I wrote:23 22 20 18 71 72 81 80 79
24 21 19 70 17 62 73 74 78
25 67 68 69 63 16 61 75 77
35 26 66 65 64 05 15 60 76
36 34 27 28 04 06 14 57 59
37 39 33 03 29 07 56 13 58
38 40 32 02 30 08 55 54 12
41 43 01 31 48 09 50 11 53
42 44 45 46 47 49 10 51 52

I thought the 11x11 puzzle from djape (here) was quite challenging, and yours doesn't fade at all in comparison, so congrats.

I wish I had the time to write a walkthrough for my logical steps, but unfortunately no. Good luck about your solver!

(PS: I remember a couple years back people have posted similar puzzles, but based on knights' move instead of kings'. Perhaps you would like to incorporate your solver for other chess pieces too.

)

by **evert** » Sat Dec 13, 2008 5:43 am

That's indeed the solution that my solver produces.

by **evert** » Sat Dec 13, 2008 6:27 am

Djape's 11x11:

Code: Select all: ... ... ... 046 ... ... ... ... ... ... 093 042 041 ... 048 052 ... ... ... ... 095 ... ... ... 039 ... ... 056 088 ... 085 096 ... ... ... ... ... ... ... ... 078 077 ... 097 023 ... ... 037 ... ... 081 ... ... ... ... ... 024 ... ... 017 ... 059 060 ... ... 101 021 ... 035 ... ... ... ... 104 ... 102 ... 121 002 ... ... 013 ... ... 105 ... 065 ... 001 ... ... ... ... ... ... ... ... 066 ... 005 ... 010 ... ... 112 ... ... ... ... 070 ... ... ... ... ... ... 114 ... 109 ... 068

I could solve it until here:

Code: Select all: 043 044 ... 046 ... ... 054 090 091 092 093 042 041 ... 048 052 ... ... ... ... 095 094 027 040 039 ... ... 056 088 ... 085 096 098 026 028 038 030 ... ... ... 078 077 099 097 023 025 029 037 031 058 081 080 079 076 100 022 024 019 036 017 032 059 060 075 074 101 021 020 035 018 033 016 061 104 103 102 073 121 002 119 034 013 015 062 105 064 065 072 001 120 003 118 012 014 111 063 106 066 071 005 004 010 011 117 112 113 110 107 067 070 006 007 008 009 116 115 114 108 109 069 068

What's the next logical step?

by **udosuk** » Sat Dec 13, 2008 2:50 pm

evert wrote:I could solve it until here:
Code: Select all
043 044 ... 046 ... ... 054 090 091 092 093 042 041 ... 048 052 ... ... ... ... 095 094 027 040 039 ... ... 056 088 ... 085 096 098 026 028 038 030 ... ... ... 078 077 099 097 023 025 029 037 031 058 081 080 079 076 100 022 024 019 036 017 032 059 060 075 074 101 021 020 035 018 033 016 061 104 103 102 073 121 002 119 034 013 015 062 105 064 065 072 001 120 003 118 012 014 111 063 106 066 071 005 004 010 011 117 112 113 110 107 067 070 006 007 008 009 116 115 114 108 109 069 068
What's the next logical step?

Highlight below to read what I wrote:089 is locked @ r2c78
Also, r4c7+r3c8 must be reserved for [082,083,084]
=> [086,087] must be @ r2c98

by **evert** » Sun Dec 14, 2008 11:08 am

BTW
Random creation of a complete grid:
This was a major problem in my program.
How it worked was: choose a random empty cell and fill it with a random number that can be placed in that cell then go on to the next random empty cell. (works fine with sudoku)
How it works now:
It tries to place the numbers in ascending order, first 1 then 2 etc, and just chooses random the cells wher to place them.
Before this it took literally hours to create a random grid.
Now it's a matter of few seconds.
I don't understand why, I'm just happy it improved.

by **evert** » Mon Dec 15, 2008 12:51 pm

udosuk wrote:Also, r4c7+r3c8 must be reserved for [082,083,084]

I missed this idea in my solver. Not anymore. Following puzzle should require a similar step:

Code: Select all: 03;..;..;..;..;..;..;27;.. ..;02;..;..;..;..;..;..;26 ..;61;..;06;08;..;11;..;22 60;..;..;..;..;14;13;..;81 ..;59;..;36;..;..;..;..;.. ..;56;..;..;16;..;..;..;.. 66;..;55;..;..;18;..;45;.. ..;..;53;50;49;..;47;..;.. ..;..;..;..;..;73;..;..;..

by **udosuk** » Mon Dec 15, 2008 4:55 pm

Thanks for a very nice puzzle!

You're right, that particular technique is very useful for this puzzle:

Highlight below to read what I wrote:03 04 __ __ __ __ __ 27 25
__ 02 05 __ __ __ __ 24 26
__ 61 __ 06 08 12 11 23 22
60 __ __ __ __ 14 13 21 81
__ 59 __ 36 __ __ __ __ __
__ 56 __ __ 16 17 19 __ __
66 __ 55 52 51 18 __ 45 __
67 54 53 50 49 48 47 __ __
68 69 70 71 72 73 74 __ __

r5c67 must be reserved for [37..44]
=> [15,20] must be @ r5c58

r2c4+r3c3 must be reserved for [28..35]
=> 7 must be @ r2c5

Afterwards, this same technique (I like to call it "bottleneck"

) can be applied a few more times near the end of the solution path.

This should be the unique solution:

Highlight below to read what I wrote:03 04 32 31 30 29 28 27 25
01 02 05 33 07 09 10 24 26
62 61 34 06 08 12 11 23 22
60 63 35 39 40 14 13 21 81
64 59 38 36 15 41 42 20 80
65 56 58 37 16 17 19 43 79
66 57 55 52 51 18 44 45 78
67 54 53 50 49 48 47 46 77
68 69 70 71 72 73 74 75 76

by **HATMAN** » Tue Dec 16, 2008 8:10 am

Evert, Matt

A couple of points:

These are succeptable to uniqueness, in short link choice and then in empty shape i.e. a four box open on one side is not possible. My temptation to shortcut significantly reduced the difficulty of DJ's 11*11.

I notice other places use odd shapes with stickyout bits - this simplyfies solution. We need to look at octagons for really difficult ones.

by **udosuk** » Tue Dec 16, 2008 3:12 pm

HATMAN wrote:These are succeptable to uniqueness, in short link choice and then in empty shape i.e. a four box open on one side is not possible. My temptation to shortcut significantly reduced the difficulty of DJ's 11*11.

I do realise it, but always try my best to not use uniqueness. I suppose a puzzle can get very difficult that forces one to make use of this info (that the solution is unique).

Another interesting issue is the usage of 180 rotational symmetry (or perhaps diagonal reflection symmetry). It is possible, but the solution space must be very narrow. :idea:

HATMAN wrote:I notice other places use odd shapes with stickyout bits - this simplyfies solution. We need to look at octagons for really difficult ones.

Speaking of which, I'm still working on a Knight Link 2 puzzle from this blog:
h-syouyuyaki.blog.drecom.jp/archive/256 { broken link }
blog.drecom.jp/h-syouyuyaki/img/256/keima.gif { broken link }

Rule (not 100% sure though due to my deficient level of Japanese):

Draw a knight's circuit through all the blue dots. Draw another knight's circuit through all the intersections without blue dots. These 2 circuits must not cross each other.

(Edited: This is obviously wrong, because you can't draw any knight's circuit through the intersections without blue dots. But you can definitely draw one through the blue dots which does not cross itself and I think the answer is unique.)

by **djape** » Wed Jan 14, 2009 8:44 pm

As of today, January 15, 2009, I'm posting Hidoku puzzles on my site on a daily basis.

by **evert** » Sat Jan 17, 2009 12:47 am

I put my solver on Djapes 9x9 20090115.

Code: Select all: 58;00;00;00;00;00;09;11;00; 00;57;56;55;00;00;00;00;12; 00;00;00;00;00;51;00;00;00; 45;00;47;00;01;04;17;00;00; 63;00;38;00;00;35;00;00;20; 00;64;00;40;00;00;00;32;00; 00;00;00;76;74;00;31;00;00; 00;66;00;00;00;72;00;00;00; 81;00;78;00;00;00;26;00;28;

For two moves it needed my manual help:
...

Code: Select all: 58;59;54;53;07;08;09;11;13 60;57;56;55;52;06;10;14;12 61;46;48;49;50;51;05;00;15 45;62;47;02;01;04;17;00;00 63;44;38;37;03;35;00;00;20 43;64;39;40;36;00;00;32;00 65;42;41;76;74;00;31;00;00 00;66;00;00;00;72;00;00;00 81;00;78;00;00;00;26;00;28

Now in cell (8,1) only 80 and 67 are allowed due to cornering.
But the consequence of putting 67 there is that 68 will go into (9,2) which would isolate
81 from 79. Therefore 80 goes into (8,1).
...

Code: Select all: 58;59;54;53;07;08;09;11;13 60;57;56;55;52;06;10;14;12 61;46;48;49;50;51;05;00;15 45;62;47;02;01;04;17;00;00 63;44;38;37;03;35;00;00;20 43;64;39;40;36;34;00;32;00 65;42;41;76;74;73;31;00;00 80;66;67;77;75;72;71;00;00 81;79;78;68;69;70;26;00;28

Now 27 can be placed in either (9,8) or (8,8).

But after placing 27 in (8,8), cornering in (9,8) would lead to
a contradiction. So 27 must go into (9,8).

I need some more work on it.

by **udosuk** » Sun Jan 18, 2009 3:42 am

Here are some suggestions on concepts to "teach" your solver some new logic to crack these steps:

evert wrote:
Code: Select all
58|59|54|53|07|08|09|11|13 60|57|56|55|52|06|10|14|12 61|46|48|49|50|51|05|..|15 45|62|47|02|01|04|17|..|.. 63|44|38|37|03|35|..|..|20 43|64|39|40|36|..|..|32|.. 65|42|41|76|74|..|31|..|.. ..|66|..|..|..|72|..|..|.. 81|..|78|..|..|..|26|..|28

Now in cell (8,1) only 80 and 67 are allowed due to cornering.
But the consequence of putting 67 there is that 68 will go into (9,2) which would isolate
81 from 79. Therefore 80 goes into (8,1).

For this, consider (9,2). It must be 79 or 80 (I called this move "bottleneck" above but on 2nd thought perhaps "gateway" is a better name. :idea:

)

Now (8,1) can't be 67 since there is no path to get to the next highest number on the board, 72 (this might be a bit tricky to implement in your solver).

Therefore there is only 1 possible cell on the board for 67: (8,3).

And then similarly only 1 possible cell on the board for 79: (9,2).

evert wrote:
Code: Select all
58|59|54|53|07|08|09|11|13 60|57|56|55|52|06|10|14|12 61|46|48|49|50|51|05|..|15 45|62|47|02|01|04|17|..|.. 63|44|38|37|03|35|..|..|20 43|64|39|40|36|34|..|32|.. 65|42|41|76|74|73|31|..|.. 80|66|67|77|75|72|71|..|.. 81|79|78|68|69|70|26|..|28

Now 27 can be placed in either (9,8) or (8,8).

But after placing 27 in (8,8), cornering in (9,8) would lead to
a contradiction. So 27 must go into (9,8).

This is easier. There are only 2 possible cells on board for 25: (8,8) & (9,8). Also they are the only 2 possible cells on board for 27. As a result, (8,8) & (9,8) must be {25,27}. (This is analogical to a "hidden pair" in sudoku solving. :idea:

)

As a result, there is only 1 possible cell on board for 29: (8,9).

And then there is only 1 possible cell on board for 30: (7,8).

Now "gateway" will force (7,9)+(8,8) to be {21..25}, leaving (9,8) as the only possible cell for 27.

:idea:

by **evert** » Tue Jan 20, 2009 11:05 am

done...
Some puzzles with bottleneck:

Code: Select all: 44;..;..;50;..;..;..;..;.. 42;45;47;..;..;70;..;64;.. ..;..;32;31;55;..;73;63;.. ..;..;..;..;..;..;74;..;62 ..;15;39;29;..;..;75;..;61 ..;..;..;..;..;..;..;01;02 ..;..;37;..;..;77;05;..;.. 21;..;23;..;..;79;..;..;.. ..;19;..;..;..;..;..;..;07 ..;..;55;..;48;10;..;..;.. 52;51;..;49;..;..;09;07;.. ..;..;..;43;..;..;13;79;.. ..;..;..;..;44;15;..;78;.. ..;..;62;..;..;..;02;01;.. ..;..;40;..;..;..;74;..;.. 37;35;..;..;20;..;24;..;.. ..;30;..;..;65;..;..;..;.. ..;..;31;27;..;..;..;..;.. ..;..;..;..;..;81;..;01;.. ..;49;..;..;09;..;02;..;.. ..;..;..;..;..;..;..;75;.. 53;..;43;07;41;..;..;..;.. ..;..;55;..;39;14;..;..;71 ..;31;..;..;..;58;16;..;70 ..;30;..;21;..;19;..;..;.. 27;..;..;22;..;..;..;66;.. ..;26;23;..;..;62;65;..;.. 55;..;..;..;..;78;..;..;.. ..;56;51;..;49;..;47;23;.. ..;..;..;..;..;..;..;44;.. ..;..;73;28;29;..;..;..;.. ..;..;61;..;..;18;..;..;41 ..;62;..;16;17;..;..;..;.. ..;63;65;..;..;..;..;..;39 ..;..;..;12;10;07;..;05;03 68;..;..;..;09;..;..;..;02

Some puzzles with pairs:

Code: Select all: ..;44;..;50;..;..;53;59;.. ..;46;45;..;51;52;..;..;.. ..;39;..;..;..;..;..;63;.. ..;..;..;..;02;..;..;..;.. ..;..;36;04;..;01;..;65;.. ..;81;19;..;23;..;..;..;28 09;..;18;..;..;..;..;68;.. ..;11;..;..;..;..;25;69;.. ..;..;..;78;..;76;..;..;.. 76;..;..;..;..;..;05;..;.. ..;..;78;..;..;04;..;..;.. ..;49;51;16;..;..;..;..;01 ..;..;52;44;..;19;..;..;10 ..;..;..;42;..;..;..;12;24 54;..;67;..;..;..;..;..;.. ..;..;57;..;36;..;38;27;.. ..;..;..;..;..;35;..;29;.. ..;..;..;59;60;..;..;..;..

This puzzle should require both:

Code: Select all: ..;..;..;..;..;..;..;53;.. 09;08;..;..;..;..;..;..;.. ..;06;13;19;..;..;..;50;.. ..;..;..;58;..;27;61;49;.. 81;..;02;..;..;..;46;..;.. ..;03;..;29;22;..;47;..;.. ..;..;..;..;..;23;..;44;.. ..;..;33;35;..;38;..;..;.. ..;..;75;..;..;..;..;..;42

by **udosuk** » Tue Jan 20, 2009 11:25 pm

Thanks for the puzzles, evert.

Have you (or your solver) tried djape's Jan 20 puzzle? Apparently it requires a new technique, which I call "path shaping". It's hard to describe the technique formally, so here is how I solved it, see if you can get the essence of that technique:

After "easy" moves:

Code: Select all: 38 37 36 12 11 .. .. 64 39 40 35 43 13 .. .. 08 21 41 42 34 44 .. .. 07 20 22 33 .. .. .. 06 01 23 19 .. .. .. 05 .. .. 24 25 .. .. .. .. .. .. 27 26 30 .. .. .. 56 .. 28 29 .. .. .. 52 .. 55

Define the following paths:
_A: 14..18 (length 5)
_B: 57..63 (length 7)
_C: 45..51 (length 7)
_D: 31..32 (length 2)

Code: Select all: 38 37 36 12 11 .. .. 64 39 40 35 43 13 .. .. 08 21 41 42 34 44 _* _* 07 20 22 33 _# _# _# 06 01 23 19 _@ _@ _@ 05 _@ .. 24 25 .. .. .. .. .. .. 27 26 30 .. .. .. 56 .. 28 29 .. .. .. 52 .. 55

_*: r3c67={_A,_B} (can be considered as a "double gateway")
_#: r4c456={_A,_B,_C}
_@: r5c3457={_A,_B,_C,_D)
=> r5c8=02
Also r4c4 (_#) can't touch r3c67 (_*)
=> r4c4 can't be from _A or _B, must be from _C=45
=> _#: r4c56={_A,_B}

Code: Select all: 38 37 36 12 11 .. .. 64 39 40 35 43 13 .. .. 08 21 41 42 34 44 _* _* 07 20 22 33 45 _# _# 06 01 23 19 _@ _@ _@ 05 _@ 02 24 25 .. .. .. .. .. .. 27 26 30 .. .. .. 56 .. 28 29 .. .. .. 52 .. 55

Now r5c7 (_@) must be from _A or _B
But it can't be from _A (too far away from 13 & 19)
=> r5c7 (_@) must be from _B
=> r4c6 (_#) must be from _B
=> r4c5 (_#) must be from _A
=> r3c6 (_*) must be from _A
=> r3c7 (_*) must be from _B
=> _@: r45c345={_A,_C,_D}

Code: Select all: 38 37 36 12 11 .. .. 64 39 40 35 43 13 .. .. 08 21 41 42 34 44 _A _B 07 20 22 33 45 _A _B 06 01 23 19 _@ _@ _@ 05 _B 02 24 25 _$ _$ .. .. .. .. 27 26 30 .. .. .. 56 .. 28 29 .. .. .. 52 .. 55

Now one of r6c34 (_$) must be from _D=31
=> r6c34 (_$) can't be both from _A
=> one of r5c34 (_@) must be from _A
(otherwise the path for _A will have at least 6 cells, too long)
=> r5c4 (_@) must be from _A
=> r5c3 (_@) must be from _D=32
=> r5c5 (_@) must be from _C=46
=> r6c3 (_$) must be from _A=18
=> r6c4 (_$) must be from _D=31

Code: Select all: 38 37 36 12 11 .. .. 64 39 40 35 43 13 .. .. 08 21 41 42 34 44 _A _B 07 20 22 33 45 _A _B 06 01 23 19 32 _A 46 05 _B 02 24 25 18 31 .. .. .. .. 27 26 30 .. .. .. 56 .. 28 29 .. .. .. 52 .. 55

Now r3c6+r4c5+r5c4 from _A must be [15..17]
=> r2c6=14
=> r2c7 must be from _B
=> r1c67=[10,09]
=> r23c7+r4c6+r5c7 from _B must be [63..60]

Code: Select all: 38 37 36 12 11 10 09 64 39 40 35 43 13 14 63 08 21 41 42 34 44 15 62 07 20 22 33 45 16 61 06 01 23 19 32 17 46 05 60 02 24 25 18 31 .. .. .. .. 27 26 30 .. .. .. 56 .. 28 29 .. .. .. 52 .. 55

Now [04,03] must be @ either r6c67 or r6c78
Gateway: r6c7 is reserved for [04,03]
Also 54 must be @ either r7c8 or r8c7
=> [59..57] can't be @ r67c8+r8c7
=> 59 can't be @ r6c8, must be @ r6c6
=> [04,03] must be @ r6c78
=> 47 must be @ r6c5

Code: Select all: 38 37 36 12 11 10 09 64 39 40 35 43 13 14 63 08 21 41 42 34 44 15 62 07 20 22 33 45 16 61 06 01 23 19 32 17 46 05 60 02 24 25 18 31 47 59 04 03 27 26 30 .. .. .. 56 .. 28 29 .. .. .. 52 .. 55

Gateway: r8c7 is reserved for [53,54]
=> 57 can't be @ r7c8 or r8c7, must be @ r7c6
=> 58 must be @ r7c5
=> [53,54] must be @ r8c7+r7c8
=> 48 must be @ r7c4
=> r8c345=[49,50,51]

Code: Select all: 38 37 36 12 11 10 09 64 39 40 35 43 13 14 63 08 21 41 42 34 44 15 62 07 20 22 33 45 16 61 06 01 23 19 32 17 46 05 60 02 24 25 18 31 47 59 04 03 27 26 30 48 58 57 56 54 28 29 49 50 51 52 53 55

Hope your solver had a easier time than me.