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AB
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 Posted: Tue Dec 20, 2005 4:17 pm Post subject: Try to solve this one - it's quite hard and challenging. |
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Hello everybody!
Please, evaluate this game.
---7-352-
7---5-4--
9---8----
---215---
-91-----3
-------4-
-1-----84
-3--941--
-76------
It was made buy AB sudoku. www.abinsigt.com |
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AB
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Dec 21, 2005 1:24 am Post subject: Not very difficult |
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I found it not difficult at all. There are some pinned squares, and two or three block - row interactions. Then, you start finding pairs, and the solution is easy to find.
I can give more details if someone wants them.
Keith |
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AB
Guest
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| Posted: Wed Dec 21, 2005 8:48 am Post subject: Re: Not very difficult |
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| keith wrote: | I found it not difficult at all. There are some pinned squares, and two or three block - row interactions. Then, you start finding pairs, and the solution is easy to find.
I can give more details if someone wants them.
Keith |
Thanks Keith. May this one would be more challenging
6-----7--
---9-----
-4------3
83-2-----
--6---18-
-9---7---
---5---9-
7--12--6-
--4-6--57 |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Wed Dec 21, 2005 10:56 am Post subject: |
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Hi,
Yup, this one suits me.
Starting from:
| Code: | 6.....7..
...9.....
.4......3
83.2.....
..6...18.
.9...7...
...5...9.
7..12..6.
..4.6..57 |
and working a little bit with the classical techniques, I got up to:
| Code: | 6 128 12389 348 1345 2358 7 124 589
. ... ..C.C ... ...a ..a. . ... Bbb
1235 128 7 9 1345 23568 568 124 568
bbbB ... . . .... ..... ... ... ...
1259 4 1289 7 15 2568 5689 12 3
..a. . .... . aA .... .... .. .
8 3 5 2 49 1 469 7 469
24 7 6 34 3459 35 1 8 249
124 9 12 6 8 7 45 3 245
23 6 238 5 7 348 2348 9 1
7 5 389 1 2 3489 348 6 48
1239 128 4 38 6 389 238 5 7 |
r3c5=5, r3c1<>5, r2c1=5, r2c1<>3, r1c3=3
r3c5=5, r1c5<>5 r1c6 <>5, r1c9=5, r1c9<>9, r1c3=9
and the last 2 statements are in contradiction.
this means 5 can be excluded from r3c5
1 in r3c5, 2 in r3c8
and I got to the:
| Code: | 6 128 12389 348 345 2358 7 14 589
. ... Babbb .C. ... .... . bC ...
1235 128 7 9 345 23568 568 14 568
59 4 89 7 1 568 5689 2 3
8 3 5 2 49 1 469 7 469
24 7 6 34 3459 35 1 8 249
aB . . Cb .... .. . . ...
124 9 12 6 8 7 45 3 245
Bab . aA . . . .. . ...
23 6 238 5 7 348 2348 9 1
7 5 389 1 2 3489 348 6 48
1239 128 4 38 6 389 238 5 7
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r6c3=2, r5c3<>1, r1c3=1, r1c8<>1, r1c8=4
r6c3=2, r5c1<>2, r5c1=4, r5c4<>4, r1c4=4
and the last 2 statements are in contradiction.
this means 2 can be excluded from r6c3
and the rest is easy up to the solution:
| Code: | 6 8 3 4 5 2 7 1 9
1 2 7 9 3 6 5 4 8
5 4 9 7 1 8 6 2 3
8 3 5 2 4 1 9 7 6
4 7 6 3 9 5 1 8 2
2 9 1 6 8 7 4 3 5
3 6 2 5 7 4 8 9 1
7 5 8 1 2 9 3 6 4
9 1 4 8 6 3 2 5 7 |
Nice exercise for applying the double implication techniques starting from pairs.
Thank you,
see u, |
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AB
Guest
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| Posted: Thu Dec 22, 2005 10:51 am Post subject: Nice solution! |
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Nice solution!
I'm impressed you've made it so quick!
Code:
+---+---+---+
|89.|..2|.3.|
|2..|...|46.|
|1..|...|.7.|
|---+---+---|
|...|.2.|...|
|.6.|1.7|...|
|...|...|38.|
|---+---+---|
|.2.|6.4|7..|
|..4|..9|5..|
|93.|..8|...|
+---+---+---+ |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Dec 22, 2005 12:46 pm Post subject: Very tough |
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This last one is very tough. I think it is beyond the capability of most people to solve, but it does have a solution.
I am not posting the solution, because I used a computer program to find it. If anyone wants a hint, let me know.
Keith |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Thu Dec 22, 2005 1:04 pm Post subject: |
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Yuuuup,
This is very, very hard, but still to be solved with the techniques of "double implication chains, starting from pairs".
Here the path to the solution:
Starting from
| Code: | 89...2.3.
2.....46.
1......7.
....2....
.6.1.7...
......38.
.2.6.47..
..4..95..
93...8... |
I found using standard techniques:
Hidden Pair 3 8 in r7c9 and r8c9,
Hidden Triple 6 4 9 in r1c5 r3c5 r6c5
and got to the position:
| Code: | 8 9 67 47 46 2 1 3 5
. . Aa .B
. . aA ..
2 57 357 3578 3578 1 4 6 9
. ..
. Ba
1 4 356 359 69 356 8 7 2
47 158 1589 3458 2 356 69 15 167
3 6 589 1 58 7 29 25 4
47 15 2 459 469 56 3 8 167
5 2 18 6 13 4 7 9 38
6 178 4 237 137 9 5 12 38
. ... . ..b
. .B. . ..b
9 3 17 257 157 8 26 4 16 |
starting from pair of digits 6,7 from r1c3:
case (A): r1c3 = 6, r1c3 <> 7, r1c4 = 7, r8c4 <> 7
case (B): r1c3 = 7, r2c2 <> 7, r8c2 = 7, r8c4 <> 7
and from (A) & (B) we can deduce: 7 not in r8c4
and from here:
| Code: | 8 9 67 47 46 2 1 3 5
2 57 357 3578 3578 1 4 6 9
1 4 356 359 69 356 8 7 2
47 158 1589 3458 2 356 69 15 167
.. a.. a... .... . ... .. Aa ...
.. ... .... .... . ... .. aA ...
3 6 589 1 58 7 29 25 4
47 15 2 459 469 56 3 8 167
.. Bb . ... ... .. . . ...
.. .. . ... ... .. . . ...
5 2 18 6 13 4 7 9 38
6 178 4 23 137 9 5 12 38
. b.. . b. ... . . aB ..
. b.. . .. ... . . Bb ..
9 3 17 257 157 8 26 4 16 |
starting from pair of digits 1,5 from r4c8:
case (A): r4c8 = 1, r4c2 and r4c3 <> 1, r6c2 = 1, r8c2 <> 1
case (B): r4c8 = 5, r4c8 <> 1, r8c8 = 1, r8c2 <> 1
and from (A) and (B) we can deduce: 1 not in r8c2
1 not in r4c3, it is in r4c2 or r6c2 (Column on 3x3 Block interaction)
| Code: | 8 9 67 47 46 2 1 3 5
2 57 357 3578 3578 1 4 6 9
. b. ... .b.. .... . . . .
. .. ... .b.B ...a . . . .
1 4 356 359 69 356 8 7 2
47 158 589 3458 2 356 69 15 167
3 6 589 1 58 7 29 25 4
. . ... . Aa . .. .. .
. . ... . aA . .. .. .
47 15 2 459 469 56 3 8 167
5 2 18 6 13 4 7 9 38
6 78 4 23 137 9 5 12 38
9 3 17 257 157 8 26 4 16
. . .. .B. .a. . .. . ..
. . .. ... ... . .. . .. |
starting from pair of digits 5,8 from r5r5:
case (A): r5c5 = 5, r9c5 <> 5, r9c4 = 5, r2c4 <> 5
case (B): r5c5 = 8, r2c5 <> 8, r2c4 = 8, r2c4 <> 5
and from (A) and (B) we deduce: 5 not in r2c4
| Code: | 8 9 67 47 46 2 1 3 5
2 57 357 378 3578 1 4 6 9
1 4 356 359 69 356 8 7 2
47 158 589 3458 2 356 69 15 167
3 6 589 1 58 7 29 25 4
47 15 2 459 469 56 3 8 167
5 2 18 6 13 4 7 9 38
. . .. . Aa . . . ..
. . .. . aA . . . aB
6 78 4 23 137 9 5 12 38
. .. . .. a.. . . Bb ..
. .. . Ba .a. . . .b ..
9 3 17 257 157 8 26 4 16 |
starting from pair of digits 1,3 from r7c5:
case (A): r7c5 = 1, r8c5 <> 1, r8c8 = 1, r8c8 <> 2
case (B): r7c5 = 3, r8c4 <> 3, r8c4 = 2, r8c8 <> 2
and from (A) and (B) we deduce: 2 not in r8c8
1 in r8c8 - Sole Candidate
5 in r4c8 6 in r9c9 - Sole Candidate
2 in r5c8 2 in r9c7 - Sole Candidate
9 in r5c7 - Sole Candidate
6 in r4c7 - Sole Candidate
3 in r4c6 - Sole Candidate
9 in r4c3 2 in r8c4 - Unique Horizontal
3 not in r2c5, it is in r2c4 or r3c4 (Column on 3x3 Block interaction)
and I got to the:
| Code: | 8 9 67 47 46 2 1 3 5
. . .. aB .. . . . .
. . .. .. .. . . . .
2 57 357 378 578 1 4 6 9
. .. ... ... .b. . . . .
. .. ... ..a bbB . . . .
1 4 356 359 69 56 8 7 2
47 18 9 48 2 3 6 5 17
.. .. . Aa . . . . ..
.. .. . aA . . . . ..
3 6 58 1 58 7 9 2 4
. . .. . bB . . . .
. . .. . Ba . . . .
47 15 2 459 469 56 3 8 17
5 2 18 6 13 4 7 9 38
6 78 4 2 37 9 5 1 38
9 3 17 57 157 8 2 4 6 |
starting from pair of digits 4,8 from r4c4:
case (A): r4c4 = 4, r1c4 <> 4, r1c4 = 7, r2c5 <> 7
case (B): r4c4 = 8, r5c5 <> 8, r2c5 = 8, r2c5 <> 7
and from (A) and (B) we deduce: 7 not in r7c5
7 not in r9c4, it is in r8c5 or r9c5 (Column on 3x3 Block interaction)
5 in r9c4 - Sole Candidate
| Code: | 8 9 67 47 46 2 1 3 5
. . .. .. .. . . . .
2 57 357 378 58 1 4 6 9
. Aa .a. ... aB . . . .
1 4 356 39 69 56 8 7 2
. . .a. .. .. .. . . .
47 18 9 48 2 3 6 5 17
.. .. . .. . . . . ..
3 6 58 1 58 7 9 2 4
. . B. . B. . . . .
47 15 2 49 469 56 3 8 17
.. .a . .. ... .. . . ..
5 2 18 6 13 4 7 9 38
. . .. . .. . . . ..
6 78 4 2 37 9 5 1 38
. B. . . .. . . . ..
9 3 17 5 17 8 2 4 6
. . .. . .. . . . . |
starting from pair in r2c2 with digit 5:
path (A): r2c2 = 5, r2c3 <> 5 and r3c3 <> 5, r5c3 = 5
path (B): r2c2 = 5, r2c5 <> 5, r5c5 = 5
and from path (A) and (B) we get twich digit 5 in row 5,
so we deduce: 5 not in r2c2
and the rest up to the following solution is easy:
| Code: | 8 9 6 7 4 2 1 3 5
2 7 5 3 8 1 4 6 9
1 4 3 9 6 5 8 7 2
4 1 9 8 2 3 6 5 7
3 6 8 1 5 7 9 2 4
7 5 2 4 9 6 3 8 1
5 2 1 6 3 4 7 9 8
6 8 4 2 7 9 5 1 3
9 3 7 5 1 8 2 4 6 |
If I counted correct, the I had to apply the technique about 6 times!
I tried to kill me ?! ... slowly ?
Nice challange.
see u, |
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Guest
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| Posted: Fri Dec 23, 2005 9:48 am Post subject: |
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Thanks!
You are the man! |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Fri Dec 23, 2005 10:39 am Post subject: |
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Hi,
There is always, someone better than me!
see u, |
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skmoejoe
Joined: 26 Oct 2005
Posts: 4
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| Posted: Fri Dec 23, 2005 4:41 pm Post subject: |
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| someone_somewhere wrote: | 6.
..4.6..57[/code]
and working a little bit with the classical techniques, I got up to:
| Code: | 6 128 12389 348 1345 2358 7 124 589
. ... ..C.C ... ...a ..a. . ... Bbb
1235 128 7 9 1345 23568 568 124 568
bbbB ... . . .... ..... ... ... ...
1259 4 1289 7 15 2568 5689 12 3
..a. . .... . aA .... .... .. .
8 3 5 2 49 1 469 7 469
24 7 6 34 3459 35 1 8 249
124 9 12 6 8 7 45 3 245
23 6 238 5 7 348 2348 9 1
7 5 389 1 2 3489 348 6 48
1239 128 4 38 6 389 238 5 7 |
r3c5=5, r3c1<>5, r2c1=5, r2c1<>3, r1c3=3
r3c5=5, r1c5<>5 r1c6 <>5, r1c9=5, r1c9<>9, r1c3=9
and the last 2 statements are in contradiction.
this means 5 can be excluded from r3c5
1 in r3c5, 2 in r3c8
and I got to the:
| Code: | 6 128 12389 348 345 2358 7 14 589
. ... Babbb .C. ... .... . bC ...
1235 128 7 9 345 23568 568 14 568
59 4 89 7 1 568 5689 2 3
8 3 5 2 49 1 469 7 469
24 7 6 34 3459 35 1 8 249
aB . . Cb .... .. . . ...
124 9 12 6 8 7 45 3 245
Bab . aA . . . .. . ...
23 6 238 5 7 348 2348 9 1
7 5 389 1 2 3489 348 6 48
1239 128 4 38 6 389 238 5 7
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, |
Can you at this point in the puzzle determine that in box 6 there is a (2,4,5) triplet r7c9 (2,4) r8c7 (45) r8c9 (245)? Or was this dumb luck?
I don't fully understand the double implication method, but I'm working on it.
Thank you. |
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someone_somewhere
Joined: 07 Aug 2005
Posts: 275
Location: Munich
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| Posted: Fri Dec 23, 2005 8:22 pm Post subject: |
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Hi,
I am color-blind, can't see small amount of red's in a big picture.
A little bit also digit-blind, can't see the triple you have not mentioned.
If I don't see it, it does not mean that it is not there.
I am also not claiming that this is the ONLY or the SHORTEST solution.
Can you point for me the "red triple" more acurate?
Thank you,
see u,
P.S. if you need some other training examples, just tell me. You could work on the "Super Tough" examples of "Krazydad" (Free Printable Sudoku Puzzles by Jim Bumgardner), but some of them are extreme difficult even for this techniques. Most of them are excellent.
[I got only up to book 8]
http://krazydad.com/sudoku/index.php?diff=ST |
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