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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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 Posted: Sat Feb 16, 2008 4:07 pm Post subject: A VVH M |
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Took some puzzles on a recent trip. This one turned out be very difficult (for me at anyrate) - don't think there's any easy path through it, tho' I've pored over it for hours, with sheets marked with all the conjugate links I can see. Comments welcome!
M4690874 (100).
| Code: |
+----------------+-----------------+-----------------+
| 5 679 367 | 23 8 2349 | 1239 12347 2349 |
| 379 79 4 | 5 1 239 | 8 237 6 |
| 8 1 2 | 6 349 7 | 39 34 5 |
+----------------+-----------------+-----------------+
| 267 2678 9 | 12378 347 12346 | 123 5 234 |
| 4 5 16 | 123 39 12369 | 1239 8 7 |
| 27 3 178 | 1278 5 1249 | 6 124 249 |
+----------------+-----------------+-----------------+
| 2367 2678 3678 | 4 37 13 | 5 9 18 |
| 1 4 5 | 9 6 8 | 7 23 23 |
| 379 789 378 | 137 2 5 | 4 6 18 |
+----------------+-----------------+-----------------+
|
The straightforward bits first. There are UR eliminations of a 6 & a 7 in the bottom-left box. And in the top right there's what I think is a WXYZ-wing, which I saw as ALS (which I suppose all XY-, XYZ-, WXYX-wings are): kills 3s in R1C78. Later, I found another pair of ALS, which eliminates the 2 in R6C9. And now I see no instantly obvious move.
I'm beginning to learn to recognise some multi-digit AICs. The following kind is not uncommon: start in a house with one number, flip out to another house, xx to a second number, back into the original house and, hey presto, one of the two numbers may be squeezed out. Here's the first one I saw. Showing some of R12, with x,.. being irrelevant number(s):
| Code: |
+------------B-----C--+-----------+--------------------+
| 3y | 23 | |
/
A / D E
| 3x | 2z --|--23w |
|
This is a 'proper' AIC: 3A=3B-3C=2C-2D=2E. The 3 in E has been squeezed out. Simplest way to put is to say that E=3 => via D,C,B, that A =3. So E =3 is false. Now, here's a question. Myth Jellies in a similar problem a few weeks ago, denigrated extended Medusa as being T&E, showing how you could use standard Medusa for this sort
of thing. But I can't see it here: there are just two conjugate links 3AB & 2DE (+the bivalue cell C), & I don't see how Medusa helps in uncovering this chain. I do see, tho', how extended Medusa will go into C & expose it.
(Oddly enough, you could eliminate the 3 in E without thinking of AICs: just look at the full grid, and you'll see that E=3 => both C =3 AND R3C5 = 3 in box 2, no matter how many 3s there are in box 1.)
The other kind of AIC that I sometimes recognise uses part of an XY-chain. Start with 4 in R1C6, on to 4 in R3C5, across to C8, down & up & back into box 2 with 2s. You'll see that this squeezes out the 2 in R1C6. And by extending the chain to C, you can also squeeze out the 3 in R1C6. All that brings us to this position ( a few numbers knocked off, but no cells yet solved).
| Code: |
+----------------+-----------------+----------------+
| 5 679 367 | 23 8 49 | 129 1247 2349 |
| 379 79 4 | 5 1 239 | 8 27 6 |
| 8 1 2 | 6 349 7 | 39 34 5 |
+----------------+-----------------+----------------+
| 267 2678 9 | 12378 347 12346 | 123 5 1234 |
| 4 5 16 | 123 39 12369 | 1239 8 7 |
| 27 3 178 | 1278 5 1249 | 6 124 49 |
+----------------+-----------------+----------------+
| 2367 278 3678 | 4 37 13 | 5 9 18 |
| 1 4 5 | 9 6 8 | 7 23 23 |
| 389 789 378 | 137 2 5 | 4 6 18 |
+----------------+-----------------+----------------+
|
I can't see anything straightforward, tho' there may well be AICs or other smart moves that I've missed. However, I did see a couple of moves that lead to a contradiction, probably disapproved of by the T&E police, perhaps found by extended Medusa as 'wraps'?:
R1C2 = 9 => R6C9 = 9. Also R1C2 = 9 => R1C6 = 4 => ... R4C3 & R3C8 both = 4.
Together, these => R6C9 = 4. This contradiction => R1C2 <> 9.
And, somewhat similarly, R7C1 = 3 leads to a contradiction. (Look at R7C3, R5C3, R5C4 & C4.)
Over to you! |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Feb 16, 2008 11:21 pm Post subject: |
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victor,
what is the original puzzle? |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Feb 16, 2008 11:30 pm Post subject: |
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SE rated this 8.3,
I am not sure that a straight forward medusa chain will work, you would probably need some extended work. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Feb 16, 2008 11:49 pm Post subject: |
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| storm_norm wrote: | victor,
what is the original puzzle? |
The original puzzle, with candidates:
| Code: | +----------------------+----------------------+----------------------+
| 35679 679 3567 | 2369 8 23469 | 1239 12347 123459 |
| 379 79 4 | 5 1 239 | 2389 237 6 |
| 8 1 2 | 369 349 7 | 39 34 3459 |
+----------------------+----------------------+----------------------+
| 267 2678 9 | 123678 347 12346 | 123 5 1234 |
| 4 5 16 | 12369 39 12369 | 1239 8 7 |
| 27 3 178 | 12789 4579 12459 | 6 124 1249 |
+----------------------+----------------------+----------------------+
| 2367 2678 3678 | 4 37 13 | 5 9 1238 |
| 1 249 35 | 39 6 8 | 7 23 23 |
| 35679 6789 35678 | 1379 2 1359 | 4 136 138 |
+----------------------+----------------------+----------------------+
http://www.menneske.no/sudoku/eng/showpuzzle.html?number=4690874
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Keith |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Feb 17, 2008 1:57 pm Post subject: |
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Victor, I just started on your puzzle, but there is definitely something wrong with the grid.
r1c3 is 8, so there can't be 8 left in the candidates for r9c1.
Let's see what I can do with the original puzzle (thx keith for posting it!) |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Feb 17, 2008 3:32 pm Post subject: |
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| Victor wrote: | Now, here's a question. Myth Jellies in a similar problem a few weeks ago, denigrated extended Medusa as being T&E, showing how you could use standard Medusa for this sort
of thing. But I can't see it here: [...] I don't see how Medusa helps in uncovering this chain. |
Here is the answer as I understand it... followed (eventually) by a solution to the puzzle.
I start with the grid after basics and color every Medusa cluster that exists in the grid, using Aa, Bb, Cc, etc., for the clusters:
| Code: |
+---------------------+----------------------+----------------------+
| 5 6g79 3D6G7 | 2U3u 8 234n9 | 1A239 1a2347P 2349s |
| 3d79r 7V9v 4 | 5 1 2M39 | 8 2m37p 6 |
| 8 1 2 | 6 34N9e 7 | 3e9E 3N4n 5 |
+---------------------+----------------------+----------------------+
| 26H7 2K678J 9 | 12378j 34n7Q 12346C | 123 5 234 |
| 4 5 1c6C | 123 3e9E 1236c9 | 1239 8 7 |
| 2W7w 3 1C78j | 1278J 5 1249s | 6 1A24 249S |
+---------------------+----------------------+----------------------+
| 2K36h7 2k678 3678 | 4 3Q7q 1b3B | 5 9 1B8b |
| 1 4 5 | 9 6 8 | 7 2f3F 2F3f |
| 379R 789r 378 | 1B37Q 2 5 | 4 6 1b8B |
+---------------------+----------------------+----------------------+
|
Next, locate every weak link between two colors. For instance, in c3 C and G are weakly linked. Other examples: DG in r1c3 and Es in b3.
Next, the pairs complementary to the weak links are strongly linked. So, from the examples above: cg, dg and eS are all strongly linked (strong inferences, not necessarily conjugates).
Next, look for pairs of strong pairs that include a color pair between them. For instance, dg and DR are strong pairs and contain the color pair Dd. So they can be combined into gR, which is also a strong pair. Keep this up (including use of the derived pairs) until you can't find any more pairs to combine. With an hour or two of work... maybe less if you don't put them in alphabetical order as I have  ... you can come up with this list of strong pairs for the clusters in this puzzle:
ac, Ad, AM, Ap, AR, Au, Av, bq, cd, cg, ch, cJ, ck, cM, cp, cu, cR, cv, dF, dg, dm, dn, dP, dq, DR, dU, En, Eq, eS, FM, fn, fq, FR, Fu, gR, Hk, jk, kw, Mn, MP, Mq, mR, mu, Nq, nR, nS, nu, PR, Pu, Pv, qr, qS, qu, RU, RV.
I point out that I haven't assumed that anything is true or false. And, I haven't made any trials. By identifying every cluster and every link between them, no trial selection of "this cluster" or "that weak link" is involved. (I can't promise, however, that I haven't made any errors!)
Now, we scan the grid again and see if any of these pairs eliminate any candidates:
| Code: |
+---------------------+-----------------------+-----------------------+
| 5 6g79 3D6G7 | 2U3u 8 -2-34n9 | 1A2-39 1a2-347P 2349s |
| 3d79r 7V9v 4 | 5 1 2M39 | 8 2m-37p 6 |
| 8 1 2 | 6 34N9e 7 | 3e9E 3N4n 5 |
+---------------------+-----------------------+-----------------------+
| 26H7 2K678J 9 | 12378j 34n7Q 12346C | 123 5 234 |
| 4 5 1c6C | 123 3e9E 1-236c9 | 1239 8 7 |
| 2W7w 3 1C78j | 1278J 5 1249s | 6 1A24 249S |
+---------------------+-----------------------+-----------------------+
| 2K36h7 2k678 3678 | 4 3Q7q 1b3B | 5 9 1B8b |
| 1 4 5 | 9 6 8 | 7 2f3F 2F3f |
| 379R 789r 378 | 1B37Q 2 5 | 4 6 1b8B |
+---------------------+-----------------------+-----------------------+
r1: Mn nu Au Fu/Pu
r2: dF/dm
r5: cM
|
There are 6 "trap" eliminations as shown. Below the grid, I have listed the strong pairs responsible for the eliminations. (Multiple possibilities for a single elimination are separated by "/".) For each of these it is possible to find an AIC by following color paths. For instance, let's take the Mn trap of <2> in r1c6:
(2-4)r1c6=(4)r3c5-(4=3)r3c8-(3=2)r8c8-(2)r2c8=(2)r2c6-(2)r1c6; r1c6<>2
The color sequence is:
2-4n=4N-4n=3N-3F=2f-2m=2M-2
Recall that I said that strong pairs such as dg and DR are combined into the strong pair gR. Well, if you kept good notes when you derived the Mn strong pair used here, you would be able to trace it back to the weak links NF and fm, which are the ones used in this AIC. For each elimination, you check your notes in this way and then follow the colored paths to find the AIC.
Let's look at the <3> elimination in r1c6 mentioned by Victor. Per my notes, the nu strong pair that provided this "trap" derived from 3 weak links: MU, fm and NF. So, we are looking for:
u=...=U-M=...=m-f=...=F-N=...=n
It is thus pretty easy to spot the AIC:
(3)r1c6-(3=2)r1c4-(2)r2c6=(2)r2c8-(2=3)r8c8-(3=4)r3c8-(4)r3c5=(4-3)r1c6; r1c6<>3
So there you have the non-T&E (if perhaps not quick or easy) way to uncover AICs with full Medusa multi-coloring.
Now, continuing with the puzzle...
The grid after those eliminations:
| Code: |
+---------------------+-----------------------+-----------------------+
| 5 6g79 3D6G7 | 2U3u 8 4n9 | 1A29 1a247P 2349s |
| 3d79r 7V9v 4 | 5 1 2M39 | 8 2m7p 6 |
| 8 1 2 | 6 34N9e 7 | 3e9E 3N4n 5 |
+---------------------+-----------------------+-----------------------+
| 26H7 2K678J 9 | 12378j 34n7Q 12346C | 123 5 234 |
| 4 5 1c6C | 123 3e9E 136c9 | 1239 8 7 |
| 2W7w 3 1C78j | 1278J 5 1249s | 6 1A24 249S |
+---------------------+-----------------------+-----------------------+
| 2K36h7 2k678 3678 | 4 3Q7q 1b3B | 5 9 1B8b |
| 1 4 5 | 9 6 8 | 7 2f3F 2F3f |
| 379R 789r 378 | 1B37Q 2 5 | 4 6 1b8B |
+---------------------+-----------------------+-----------------------+
|
We can now extend some clusters. For instance, we have 9N in r1c6.
But, that's not all we can do. Notice that some disparate colors are now strongly linked due to eliminations. For instance the 2U and 2M in b2 are now strongly linked. This means that we can combine the Mm and Uu clusters into a single cluster. I will retain the letter that is first alphabetically. So, U becomes m and u becomes M. We also make those substitutions in our list of strongly linked pairs (e.g., RU becomes mR, which is a new strong pair and may provide additional eliminations).
So, once we have extended and combined clusters wherever possible and identified all new weak links and then combined the resulting list of strong pairs into all new possible strong pairs, we get here (provided again that I haven't made any errors in following these steps that assure that I am avoiding all trials and truth assumptions):
| Code: |
+---------------------+-----------------------+-----------------------+
| 5 6g79 3D6G7 | 2m3M 8 4F9f | 1A29 1a247P 2349s |
| 3d79r 7V9v 4 | 5 1 2M3D9 | 8 2m7p 6 |
| 8 1 2 | 6 34f9e 7 | 3e9E 3f4F 5 |
+---------------------+-----------------------+-----------------------+
| 26H7 2K678J 9 | 12378j 34F7Q 12346C | 123 5 234 |
| 4 5 1c6C | 123 3e9E 136c9 | 1239 8 7 |
| 2W7w 3 1C78j | 1278J 5 1249s | 6 1A24 249S |
+---------------------+-----------------------+-----------------------+
| 2K36h7 2k678 3678 | 4 3Q7q 1b3B | 5 9 1B8b |
| 1 4 5 | 9 6 8 | 7 2f3F 2F3f |
| 379R 789r 378 | 1B37Q 2 5 | 4 6 1b8B |
+---------------------+-----------------------+-----------------------+
|
Strong pairs: ac, Ad, AM, Ap, AR, Av, bd, bq, bR, cd, cg, ch, cJ, ck, cM, cp, cR, cv, dF, dg, dm, dP, dq, DR, EF, Eq, eS, FM, fq, FR, FS, gR, Hk, jk, kw, MP, Mq, mR, PR, Pv, qr, qS, RV.
There are really only two new strong pairs here: bd and bR. And neither leads to any eliminations. So, we've reached the end of the road for this approach alone. The next step is to search for some strong additional strong inferences in the grid to exploit. Following the XY Chain sequence beginning in r2c2 we can get some strong inferences. First, (9)r2c2=(2)r2c8; thus we have the strong pair mv. r29c8 give us Fp. The 3-cell chain gives us Fv. And now...
Additional strong pairs: Fp, Fv, mv, pq, qv.
None of this leads to any additional eliminations. So, time to abandon strict Medusa. (And just when it was starting to get fun! )
So now, I start by invoking the r29c12 {79} UR to remove <7> from r9c1. Then, some "extended" Medusa, starting in r5c3:
| Code: |
+--------------------+----------------------+-------------------+
| 5 6r79 367r | 23r 8 49 | 129 1r247 2349 |
| 3r79 79r 4 | 5 1 2r39 | 8 27r 6 |
| 8 1 2 | 6 349 7 | 39 34 5 |
+--------------------+----------------------+-------------------+
| 2r67 2678r 9 | 12378 347 12346R | 123 5 234 |
| 4 5 1G6R |-12r3 39 1r-3-6G9 |-1239 8 7 |
| 27r 3 1R78 | 1278r 5 1249 | 6 124 249 |
+--------------------+----------------------+-------------------+
| 236r7 2r678 3678 | 4 37r 13r | 5 9 1r8 |
| 1 4 5 | 9 6 8 | 7 23 23 |
| 39r 7r89 378 | 1r37 2 5 | 4 6 18r |
+--------------------+----------------------+-------------------+
|
This is about all that this start provides. So, I restart at r3c8:
| Code: |
+---------------------+---------------------+---------------------+
| 5 67-9 367 | 23r 8 4G9R | 12-9 1247 2-349g|
| 3r79 79r 4 | 5 1 2r39 | 8 27r 6 |
| 8 1 2 | 6 34R9 7 | 39r 3R4G 5 |
+---------------------+---------------------+---------------------+
| 267 2678 9 | 12378 34G7 12346 | 12-3 5 23g4 |
| 4 5 16 | 2r3 39r 16 | 23r9 8 7 |
| 27 3 178 | 1278 5 1249 | 6 124 -24g9r |
+---------------------+---------------------+---------------------+
| 2367 2678 3678 | 4 37 13 | 5 9 18 |
| 1 4 5 | 9 6 8 | 7 2R3G 2G3R |
| 39 789 378 | 137 2 5 | 4 6 18 |
+---------------------+---------------------+---------------------+
|
Eliminations and promotions...
| Code: |
+---------------------+---------------------+---------------------+
| 5 67 367 | 23r 8 4G9R | 12 1247 249G |
| 3r79 79r 4 | 5 1 2r39 | 8 27r 6 |
| 8 1 2 | 6 -34R9G 7 | 3G9R 3R4G 5 |
+---------------------+---------------------+---------------------+
| 267 2678 9 | 12378 34G7 12346 | 12 5 23G4 |
| 4 5 16 | 2r-3 3G9R 16 | 23R9 8 7 |
| 27 3 178 | 1278 5 1249 | 6 124 4G9R |
+---------------------+---------------------+---------------------+
| 2367 2678 3678 | 4 37 13 | 5 9 18 |
| 1 4 5 | 9 6 8 | 7 2R3G 2G3R |
| 39 789 378 | 137 2 5 | 4 6 18 |
+---------------------+---------------------+---------------------+
|
And then, more extended Medusa plus a Finned X-Wing in c15 that removes <7> from r4c2:
| Code: |
+-------------------+------------------+------------------+
| 5 6g7 67g | 3 8 4G9R | 12 124 249G |
| 3 9 4 | 5 1 2 | 8 7 6 |
| 8 1 2 | 6 4R9G 7 | 3G9R 3R4G 5 |
+-------------------+------------------+------------------+
| 267 26-78 9 | 178 34G7 1346 | 12 5 23G4 |
| 4 5 16 | 2 3G9R 16 | 3R9G 8 7 |
| 2r7 3 178 | 178 5 149G | 6 124 4G9R |
+-------------------+------------------+------------------+
| 267 2r-6-78 678 | 4 37g 13g | 5 9 1g8 |
| 1 4 5 | 9 6 8 | 7 2R3G 2G3R |
| 9 7g8 3 | 1g7 2 5 | 4 6 18g |
+-------------------+------------------+------------------+
|
And more extended Medusa starting in r7c5:
| Code: |
+------------------+------------------+------------------+
| 5 6G7R 6R7G | 3 8 49r | 12 124 2r49 |
| 3 9 4 | 5 1 2 | 8 7 6 |
| 8 1 2 | 6 4r9 7 | 39 34 5 |
+------------------+------------------+------------------+
| 2r67 26R8 9 | 178r 347R 13R46| 1r2 5 234r |
| 4 5 1r6 | 2 39r 16r | 3r9 8 7 |
| 27r 3 178r | 1r78 5 14r9 | 6 #12r4 49r |
+------------------+------------------+------------------+
| 26r-7 2r8 67r8 | 4 3R7G 1R3G | 5 9 1G8R |
| 1 4 5 | 9 6 8 | 7 #2r3 23r |
| 9 7G8R 3 | 1G7R 2 5 | 4 6 1R8G |
+------------------+------------------+------------------+
|
An "r" wrap in c8 means R is false and Gg is true. But, this doesn't solve the puzzle.
There is now an XY Wing with r4c2 pivot that finally solves the puzzle.
| Code: |
+---------------+---------------+---------------+
| 5 6 7 | 3 8 49 | 12 124 249 |
| 3 9 4 | 5 1 2 | 8 7 6 |
| 8 1 2 | 6 49 7 | 39 34 5 |
+---------------+---------------+---------------+
| 26-7 28 9 | 78 34 146 | 12 5 234 |
| 4 5 16 | 2 39 16 | 39 8 7 |
| 27 3 18 |-78 5 149 | 6 124 49 |
+---------------+---------------+---------------+
| 26 28 68 | 4 7 3 | 5 9 1 |
| 1 4 5 | 9 6 8 | 7 23 23 |
| 9 7 3 | 1 2 5 | 4 6 8 |
+---------------+---------------+---------------+
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Wed Feb 20, 2008 3:34 pm Post subject: |
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I often admire smart bits of logic & think "Wish I'd thought of that." But this is in a different league. I guess I feel a bit like an amateur in a village football team watching a world-class player at work - masterly!
(Asellus, do please note that I wasn't in the slightest maligning extended Medusa. I glanced at a (slightly bad-tempered) thread in another forum about what is and what is not 'T & E' and didn't really understand it.)
One moral for me, I guess, is to walk away from puzzles that are just plain out of my league - Storm_norm sensibly did that in another thread when he posted 2 OK puzzles & one very difficult one. Still, next time I meet one I'll have a go - maybe. Anyway, thanks for the lesson. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Feb 20, 2008 6:35 pm Post subject: |
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| Victor wrote: | | Asellus, do please note that I wasn't in the slightest maligning extended Medusa. |
Don't worry: I don't have any ego wrapped up in sudoku!
Besides, "extended" Medusa can be justly criticized. It is true, for instance, that in the case of a "wrap" extended color markings remain that are no longer useful and need to be erased. That is at least a bit less than elegant. I just tend to find the arguments for "purity" to be rather overstated.
I wouldn't recommend the "pure" application of Medusa multi-coloring as demonstrated above as a technique for folks who actually want to enjoy doing sudoku... unless grinding through hours of tedious mechanical detail is what turns you on. In that case, go for it!
I actually feel that Medusa multi-coloring, of a more selective and judicious sort (and thus involving some element of T&E) is an excellent technique and is worth considering before resorting to the "extended" approach. Except in the simplest cases, it's not very good for P&P, however, since so many color symbols can be required.
Anyway, I'm glad you found it all interesting. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Feb 20, 2008 7:22 pm Post subject: |
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| Asellus wrote: | | Victor wrote: | | Asellus, do please note that I wasn't in the slightest maligning extended Medusa. |
Don't worry: I don't have any ego wrapped up in sudoku!
Besides, "extended" Medusa can be justly criticized. It is true, for instance, that in the case of a "wrap" extended color markings remain that are no longer useful and need to be erased. That is at least a bit less than elegant. I just tend to find the arguments for "purity" to be rather overstated.
I wouldn't recommend the "pure" application of Medusa multi-coloring as demonstrated above as a technique for folks who actually want to enjoy doing sudoku... unless grinding through hours of tedious mechanical detail is what turns you on. In that case, go for it!
I actually feel that Medusa multi-coloring, of a more selective and judicious sort (and thus involving some element of T&E) is an excellent technique and is worth considering before resorting to the "extended" approach. Except in the simplest cases, it's not very good for P&P, however, since so many color symbols can be required.
Anyway, I'm glad you found it all interesting. |
I can't resist tossing in my 2¢, and that's probably what it's worth.
When I first started seeing grids using Medusa, I was intimidated and figured it was beyond my capabilities. But then Keith wrote his introduction to it and it wasn't so hard after all. After a couple of questions, I was regularly solving puzzles with it.
Then you, Asellus, wrote up extended Medusa and I asked a bunch of questions and was soon using that to solve a lot of puzzles. Both the regular and extended are very conducive to P&P guys like me, although I only deal with two colors. Still, even with that limitation, it's very powerful.
I do view both the regular and extended as T&E, albeit much more fun and satisfying than simpler forms of T&E, like testing each number of a bivalue cell.
Maybe someday I'll graduate to AIC and Eureka notation, but don't hold your breath!! |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Feb 20, 2008 9:18 pm Post subject: |
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| Quote: | | I wouldn't recommend the "pure" application of Medusa multi-coloring as demonstrated above as a technique for folks who actually want to enjoy doing sudoku... unless grinding through hours of tedious mechanical detail is what turns you on. In that case, go for it! |
can I make an anaolgy here??
A hole in one. you really can only take personal pride in making the shot. even if it took hour upon hour of practice to make it.
norm |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Fri Feb 22, 2008 1:42 pm Post subject: |
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You Medusa missionaries have just about convinced me! But I did also take to heart Nataraj's advice / example from a previous thread, to use Medusa to spot AICs.
Being an AIC missionary: finding and expressing a chain is very satisfying. (But I don't personally like Eureka.)
Apologies for apparently getting one of the grids wrong. Guess I was so fed up with this puzzle that I got careless. |
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