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April 17, 2006: Type 1 / 6 Unique Rectangle

 
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keith
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Joined: 07 Feb 2006
Posts: 35
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 17, 2006 1:58 am    Post subject: April 17, 2006: Type 1 / 6 Unique Rectangle Reply with quote

Today's Nightmare has a Unique Rectangle which permits both Type 1 and Type 6 reductions.

Starting from

003000004000900078060005000005043010000010000020650800000500020690001000700000900

we reach

Code:


+----------------+----------------+----------------+
| 2589 78   3    | 1    2678 2678 | 256  569  4    |
| 25   14e  14f  | 9    236  26   | 2356 7    8    |
| 289  6    79   | 4    2378 5    | 123  39   129  |
+----------------+----------------+----------------+
| 89   78   5    | 27   4    3    | 267  1    2679 |
| 34a  34b  6    | 278  1    2789 | 257  59   2579 |
| 1    2    79   | 6    5    79   | 8    4    3    |
+----------------+----------------+----------------+
| 34c  134d 148g | 5    9    4678 | 1467 2    167  |
| 6    9    248  | 2378 278  1    | 3457 358  57   |
| 7    5    1248 | 238  268  2468 | 9    368  16   |
+----------------+----------------+----------------+



abcd is a Type-1 UR, so d = <1>.

abcd is also an X-wing on <3>, so b = c = <3>.

There is another UR in defg.

Also, there is an Empty Rectangle (ER) which removes <9> in R3C9. (No matter where the <9> falls in R4, R3C9 is not <9>.) This ER breaks the puzzle wide open. Look at

http://www.sudoku.com/forums/viewtopic.php?t=3251

Best wishes,

Keith
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Myth Jellies
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Joined: 04 Apr 2006
Posts: 42

PostPosted: Mon Apr 17, 2006 4:46 am    Post subject: Reply with quote

Congratulations, you have actually found a useful MUG-Lite (Multi-value Universal Grave as opposed to bivalue). As two BUG-Lites joined at a single cell, abcdefg forms a MUG-Lite with a type 1 reduction that means cell g equals 8. Nice find.
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keith
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Joined: 07 Feb 2006
Posts: 35
Location: near Detroit, Michigan, USA

PostPosted: Mon Apr 17, 2006 5:25 am    Post subject: Reply with quote

MJ,

Yes, I noticed that the Type-6 reduction on abcd leads to a Type-1 reduction on defg which means g = <8>.

I did not have a name for it, and did not see it as a single pattern.

In the situation I posted, I did not see any immediate reductions of defg, if you ignore abcd. It also seems, though I have not looked closely, that the Type-1 reduction of abcd destroys the UR of defg, so g = <8> is not immediately found.

Best wishes,

Keith
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