The New Sudoku Players' Forum

by **ravel** » Wed Jul 19, 2006 9:21 am

RW wrote:... (#36). There is at least 5 different URs that allow eliminations (and a BUG-lite) ...

Code: Select all: 1 2 3 | 9 5 67 | 4 8 67 69 468 46 | 1 378 2367 | 237 5 679 569 568 7 | 4 38 236 | 23 269 1 ---------------------------------------------- 57 57 8 | 3 1 9 | 6 4 2 36 36 9 | 2 4 8 | 1 7 5 4 1 2 | 7 6 5 | 9 3 8 ---------------------------------------------- 8 67 1 | 5 9 4 | 27 26 3 367 3467 46 | 8 2 1 | 5 69 679 2 9 5 | 6 37 37 | 8 1 4

Which one am i missing?
What i saw was:
UR4 36 in r48c12: r8c12<>6
UR4 46 in r28c23: r28c2<>6
UR 37 in r29c56: r2c6<>3
UR 23 in r23c67: r23c6<>3

r8c9=6 => r8c8=9 => (r7c8<>6)r3c8=6 => r2c9=9 => r2c1=6 => r3c1=9
=> r8c9<>6

But nothing solved it.

by **Carcul** » Wed Jul 19, 2006 10:44 am

Ravel wrote:UR4 36 in r48c12: r8c12<>6
UR4 46 in r28c23: r28c2<>6

We can use those two URs in another way, by noting that, if r7c2=7 then r2c2 must be "8". But:

[r7c7]=7=[r7c2]=8=[r2c2]=4=[r8c2]=3=[r8c1]-3-[r5c1]-6-[r2c1]-9-
-[r2c9]=9=[r8c9]=7=[r7c7], => r7c7=7 which solve the puzzle.

This deduction makes use of a concept that I use for some time and that I call "Two Incompatible Unique Rectangles" (TIUR).

Ravel wrote:UR 37 in r29c56: r2c6<>3
UR 23 in r23c67: r23c6<>3

Using that concept, we can use these two URs in an interesting deduction that, unfortunately, doesn't solve the puzzle. Note that if r1c6=6 then r3c5 cannot be "8". But:

r1c6=6 => Naked Pair in cells r3c67 => r3c5<>3 => r3c5=8.

So r1c6<>6.

Carcul

by RW » Wed Jul 19, 2006 5:49 pm

ravel wrote:
Code: Select all
1 2 3 | 9 5 67 | 4 8 67 69 468 46 | 1 378 2367 | 237 5 679 569 568 7 | 4 38 236 | 23 269 1 ---------------------------------------------- 57 57 8 | 3 1 9 | 6 4 2 36 36 9 | 2 4 8 | 1 7 5 4 1 2 | 7 6 5 | 9 3 8 ---------------------------------------------- 8 67 1 | 5 9 4 | 27 26 3 367 3467 46 | 8 2 1 | 5 69 679 2 9 5 | 6 37 37 | 8 1 4

Which one am i missing?

There's a UR+2k in r12c69 + r2c1 (r2c6<>6). This is how far I got when trying to solve the puzzle, but unfortunately this doesn't solve it either. To solve it you must use one of the URs you already mentioned as a +2k variant (include one extra bivalue cell).

RW

by **ravel** » Wed Jul 19, 2006 7:57 pm

Ah, thats nice, r2c1 is the extra cell (and r7c2 for the other)

But does it classify, when it needs 2 UR's (the nice it is) ?

PS: i saw now that eliminating 3 from r8c2 (with the extra cell r7c2) alone solves the puzzle.

by RW » Thu Jul 20, 2006 6:00 am

Very good ravel! Did you also see the BUG-lite in r2c19, r3c18 and r8c89 (r8c9<>6)?

Even if this is a nice puzzle, I'm not sure if it should be on the list. If a puzzle is solvable by a collection of easier techniques than the extreme move, then it shouldn't qualify. This puzzle solves with one UR type 4 and a XY-wing, the xy-wing is in the same cells as the UR+2kx and makes the same elimination. This solution is very easy to find while the UR+2kx has proven to be quite hard...

RW

by RW » Fri Jul 21, 2006 5:16 pm

Here's another sneaky UR in a fully symmetrical puzzle. I'm not adding it to the list, as there is already so many URs and this puzzle also has several alternative ways to reach the solution (BUG-lite+1 + X-wing + UR type 4, or BUG-lite+1 + XY-wing, or X-wing + XY-wing + UR type 1 + BUG-lite+2 + XY-wing). But, it is also solvable by singles + locked candidates (once is enough) + one UR. Enjoy!

Code: Select all: *-----------* |..1|9.2|3..| |...|...|...| |6..|318|..4| |---+---+---| |8.5|...|6.7| |..2|...|5..| |4.6|...|8.1| |---+---+---| |2..|196|..3| |...|...|...| |..9|5.3|1..| *-----------*

RW

by RW » Fri Jul 21, 2006 8:32 pm

I just added another fully symmetrical puzzle under the title 'Advanced BUG-lite':

Code: Select all: ..36.49.....7.2...6.......435.....98.........82.....755.......6...9.7.....12.68..

The intended solution combines a BUG-lite+some strong links with a XY-chain. I'm sure none of your solvers will find this move, but IMO it's actually easier than finding a normal XY-chain, because when I smell the BUG-lite I know where to start the chain. Good luck!

Edit: And I added a BUG-lite+1 for those who want to practise on something easier first.

RW

by ab » Sat Jul 22, 2006 11:39 pm

here's one with an xyz wing.

Code: Select all: . . 4 | . 3 . | 6 8 2 . . . | 9 . . | . . 7 7 . . | . 4 . | . . 3 ------+-------+------ . 3 . | . . . | . . . 5 . 7 | . . . | 1 . 8 . . . | . . . | . 4 . ------+-------+------ 8 . . | . 5 . | . . 4 9 . . | . . 7 | . . . 4 1 3 | . 9 . | 7 . .

by RW » Sun Jul 23, 2006 8:21 am

Thanks ab! At first it seemed that the puzzle could be a very good candidate to reveal a Reverse BUG elimination (26), but unfortunately I couldn't find any. But the XYZ-wing solved it nicely, puzzle added to the list.

RW

by **ravel** » Mon Jul 24, 2006 9:02 am

RW wrote:
Code: Select all
*-----------* |..1|9.2|3..| |...|...|...| |6..|318|..4| |---+---+---| |8.5|...|6.7| |..2|...|5..| |4.6|...|8.1| |---+---+---| |2..|196|..3| |...|...|...| |..9|5.3|1..| *-----------*

I saw the UR elimination (2 numbers in r9c9), but i could not find a BUG-lite+1. Can you point me to it, please?

Code: Select all
..36.49.....7.2...6.......435.....98.........82.....755.......6...9.7.....12.68..

Solved it with a UR type 4 and a UR+2kx (elimination in r5c8) and BUG+1, again was blind for the BUG-lite+.

by **Carcul** » Mon Jul 24, 2006 10:41 am

Ravel wrote:I saw the UR elimination (2 numbers in r9c9), but i could not find a BUG-lite+1. Can you point me to it, please?

The AUR in cells r19c89 solves the puzzle. Also, you have a BUG-lite+1 in cells r456c26 that forces r6c6=5 (and that also solve the puzzle in conjunction with the UR in r46c58).

Carcul

by **ravel** » Mon Jul 24, 2006 11:08 am

Carcul wrote:Also, you have a BUG-lite+1 in cells r456c26 that forces r6c6=5

Thanks, but i thought there is one without using an x-wing.

RW wrote:... BUG-lite+1 + X-wing + UR type 4, or BUG-lite+1 + XY-wing ...

(Hm, thought i had already posted this:) Either the x-wing or the xy-wing has to be applied (with a hidden pair) to get the BUG-lite+1.

by RW » Mon Jul 24, 2006 9:29 pm

ravel wrote:Either the x-wing or the xy-wing has to be applied (with a hidden pair) to get the BUG-lite+1.

After singles, and a hidden pair:

Code: Select all: *-----------------------------------------------------------* | 5 48 1 | 9 467 2 | 3 678 68 | | 9 3 48 | 467 4567 457 | 27 1 268 | | 6 2 7 | 3 1 8 | 9 5 4 | |-------------------+-------------------+-------------------| | 8 *19 5 | 24 234 *19 | 6 23 7 | | 3 *17 2 | 678 678 *17 | 5 4 9 | | 4 *79 6 | 27 2357 *79+5 | 8 23 1 | |-------------------+-------------------+-------------------| | 2 5 48 | 1 9 6 | 47 78 3 | | 1 6 3 | 2478 2478 47 | 247 9 5 | | 7 48 9 | 5 248 3 | 1 268 268 | *-----------------------------------------------------------* r6c6=5

Then some more singles and one box/line interaction gets here

Code: Select all: *-----------------------------------------------------------* | 5 48 1 | 9 467 2 | 3 678 68 | | 9 3 48 | 467 5 *47 |*27 1 268 | | 6 2 7 | 3 1 8 | 9 5 4 | |-------------------+-------------------+-------------------| | 8 1 5 | 24 234 9 | 6 23 7 | | 3 7 2 | 68 68 1 | 5 4 9 | | 4 9 6 | 27 237 5 | 8 23 1 | |-------------------+-------------------+-------------------| | 2 5 48 | 1 9 6 | 47 78 3 | | 1 6 3 | 2478 2478 -47 |*24 9 5 | | 7 48 9 | 5 248 3 | 1 268 268 | *-----------------------------------------------------------* r8c6<>4

Puzzle then solves with singles. And as you both pointed out, the UR in r19c89 solves the puzzle in one step. Well done!

I know the Advanced BUG-lite is tough, I could probably have found an easier one. But it's definitely not any harder than manually spotting ALS-eliminations in a grid with few solved cells. This advanced BUG-lite technique is actually one that I use all the time, sort of AUR extended to 'almost BUG-lite'. I can give you a hint: the possible deadly pattern is in r357c23. As it is with some strong links it allows one immediate elimination (r5c3<>7), but ignore that. You would only destroy the pattern for the move that solves the puzzle. Instead look for some interaction with a few bivalue cells. The xy-chain is actually quite long if examined as a normal xy-chain (7 cells), but only four steps is needed if you read the hidden singles instead of naked singles (like I usually do).

Good luck!
RW

by **ravel** » Mon Aug 07, 2006 8:35 am

Code: Select all: +-------+-------+-------+ | . . 7 | . . . | . . . | | . . . | . 3 4 | . 7 6 | | . . . | 1 . 7 | 5 . 3 | +-------+-------+-------+ | 2 . . | 3 . . | . . 8 | | 8 . . | . . . | . . 5 | | 5 . . | . . 6 | . . 1 | +-------+-------+-------+ | 6 . 8 | 4 . 2 | . . . | | 3 4 . | 7 6 . | . . . | | . . . | . . . | 4 . . | +-------+-------+-------+

by RW » Mon Aug 07, 2006 9:55 am

ravel wrote:
Code: Select all
+-------+-------+-------+ | . . 7 | . . . | . . . | | . . . | . 3 4 | . 7 6 | | . . . | 1 . 7 | 5 . 3 | +-------+-------+-------+ | 2 . . | 3 . . | . . 8 | | 8 . . | . . . | . . 5 | | 5 . . | . . 6 | . . 1 | +-------+-------+-------+ | 6 . 8 | 4 . 2 | . . . | | 3 4 . | 7 6 . | . . . | | . . . | . . . | 4 . . | +-------+-------+-------+

r5c5=9 and the puzzle is solved...

Very interesting technique! I must digest it for a while, but Gurths theory seems to be quite waterproof.

RW

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