The New Sudoku Players' Forum

by **ArkieTech** » Fri Jul 12, 2019 10:55 am

Code: Select all: *-----------* |...|.4.|...| |..2|6.5|7..| |.3.|...|.1.| |---+---+---| |6..|...|..5| |.4.|...|.8.| |..5|2.9|6..| |---+---+---| |.8.|.1.|.4.| |9..|.2.|..1| |...|...|...| *-----------*

by **SteveG48** » Fri Jul 12, 2019 12:47 pm

Code: Select all: *--------------------------------------------------* | 8 6 9 | 17 4 17 | 23 5 23 | | 4 1 2 | 6 3 5 | 7 9 8 | | 5 3 7 | 8 9 2 | 4 1 6 | *----------------+----------------+----------------| | 6 9 8 | 34 7 c34 | 1 2 5 | | 2 4 3 | 15 56 16 | 9 8 7 | | 1 7 5 | 2 8 9 | 6 3 4 | *----------------+----------------+----------------| |b37 8 6 | 59 1 c37 | 25 4 29 | | 9 5 4 | 37 2 c68 | 38 67 1 | |a37 2 1 | 459 5-6 c468 | 358 a67 39 | *--------------------------------------------------*

(6=37)r9c18 - 3r7c1 = (3468)r4789c6 => -6 r9c5 ; stte

Looking forward to a good BUG+3. I can get 2 eliminations easily, but they don't solve the puzzle

.

by **SpAce** » Fri Jul 12, 2019 2:14 pm

Code: Select all: .----------.-------------------------.---------------. | 8 6 9 | c17 4 d(1)7 | 23 5 23 | | 4 1 2 | 6 3 5 | 7 9 8 | | 5 3 7 | 8 9 2 | 4 1 6 | :----------+-------------------------+---------------: | 6 9 8 | 34 7 34 | 1 2 5 | | 2 4 3 | 15 56 d(16) | 9 8 7 | | 1 7 5 | 2 8 9 | 6 3 4 | :----------+-------------------------+---------------: | 37 8 6 | 59 1 37 | 25 4 29 | | 9 5 4 | c37 2 8-6 | b38 67 1 | | 37 2 1 | a49[+5] a[56] a48[+6] | a58+3 67 39 | '----------'-------------------------'---------------'

BUG+3

(65==3)r9c4567 - r8c7 = (37-1)r81c4 = (16)r15c6 = > -6 r8c6; stte

3D-Medusa (22 immediate placements): Show

Edit: a minor cosmetic change to the chain.

by **SpAce** » Fri Jul 12, 2019 4:34 pm

SteveG48 wrote:Looking forward to a good BUG+3.

Oh, it was supposed to be good too? Dunno about that, but at least it's a BUG+3 (unless I made mistakes)

I can get 2 eliminations easily, but they don't solve the puzzle .

You have to aim well to do that, as there's only a 36% chance of hitting a non-stte candidate!

If I counted correctly, there are 18 stte-candidates and 10 other valid eliminations, and those groups correspond with the two available Medusa clusters almost directly. The larger cluster (hidden in my previous post) contains all the stte-candidates, and the smaller one has 8 of the less useful ones. Two are in neither group, and they're the least helpful.

The smaller cluster doesn't solve with mere Medusa techniques anyway, and even if solved (via a more advanced coloring or otherwise), it won't solve the puzzle (but it gives you BUG+1). On the other hand, eliminating any one of the bigger cluster's false candidates does solve the puzzle, and it also solves with Medusa directly. Here's the complementary smaller cluster:

the smaller Medusa cluster: Show

If you determine that the "-parity is false (or just eliminate any one of the "-candidates), it gives you 6 placements and BUG+1, but no stte.

The weakest eliminations are the two false BUG guardians which belong to neither Medusa cluster: -3 r9c7, -5 r9c4. Of course, killing them both gives you BUG+1, and killing just 3r9c7 gives a very easy BUG+2, so they're not totally useless either.

PS. This Medusa analysis was just an after-thought. I didn't really use it to solve this puzzle, but in more complicated cases it's a useful tool as it can tell a lot about a puzzle. Most of the time it also removes the need to look up stte-candidate lists (which I hate to do, unless that list is very small and hard to locate otherwise).

PPS. Had I written my chain like this:

Code: Select all: (65)r9c456 == (3)r9c7 - r8c7 = (37-1)r81c4 = (16)r15c6 => -5 r9c7 (1st link), -6 r8c6; stte

...it would have solved both Medusa clusters at once. Of course it doesn't matter because -6r8c6 solves them both eventually, but not the other way around. Too bad, because this would be much prettier if only it were stte:

Code: Select all: (56)r9c456 == (3)r9c7 => -5 r9c7; BUG+1

by **Ngisa** » Fri Jul 12, 2019 6:32 pm

Code: Select all: +--------------+------------------+-----------------+ | 8 6 9 | 17 4 17 | 23 5 23 | | 4 1 2 | 6 3 5 | 7 9 8 | | 5 3 7 | 8 9 2 | 4 1 6 | +--------------+------------------+-----------------+ | 6 9 8 |e34 7 d34 | 1 2 5 | | 2 4 3 | 15 56 16 | 9 8 7 | | 1 7 5 | 2 8 9 | 6 3 4 | +--------------+------------------+-----------------+ | 37 8 6 | 59 1 37 | 25 4 29 | | 9 5 4 | 7-3 2 68 |a38 67 1 | | 37 2 1 | 459 56 c468 |b358 67 39 | +--------------+------------------+-----------------+

(3=8)r8c7 - r9c7 = (8-4)r9c6 = r4c6 - (4=3)r4c4 => - 3r8c4; stte

Clement

by **SteveG48** » Fri Jul 12, 2019 8:14 pm

SpAce wrote:BUG+3

(65==3)r9c4567 - r8c7 = (37-1)r81c4 = (16)r15c6 = > -6 r8c6; stte

Ask and ye shall receive.

by **eleven** » Fri Jul 12, 2019 10:29 pm

Code: Select all: *----------------------------------------------------* | 8 6 9 | a17 4 7-1 | 23 5 23 | | 4 1 2 | 6 3 5 | 7 9 8 | | 5 3 7 | 8 9 2 | 4 1 6 | |-------------+-------------------+------------------| | 6 9 8 | 34 7 34 | 1 2 5 | | 2 4 3 | 5-1 56 e16 | 9 8 7 | | 1 7 5 | 2 8 9 | 6 3 4 | |-------------+-------------------+------------------| | 37 8 6 | 59 1 37 | 25 4 29 | | 9 5 4 | b37 2 d68 | c38 67 1 | | 37 2 1 | 459 56 468 | 358 67 39 | *----------------------------------------------------*

The standard solution is an xy-chain
(1=73)r18c4 - (3=86)r8c76 - (6=1)r5c6 => -1r5c4,r1c6
In some way you use it for the 3r9c7 case:

Code: Select all: (65==3)r9c4567 - r8c7 = (37-1)r81c4 = (16)r15c6 = > -6 r8c6; stte 8r8c6 = (8-3)r8c7 = (37-1)r81c4 = (16)r15c6 = > -6 r8c6; stte

For the 1r5c4 elimination 5r9c4 would be the "hardest" candidate.
5r9c4 - (5=68)b8p76 - (8=37)r8c74 - (7=1)r1c4
6r9c6 - (6=1)r5c6
3r9c7 - (3=86)r8c67 - (6=1)r5c4

In any case the BUG needs a shorter contradiction, which solves the puzzle. (like a UR, where the external candidates are a pair of the UR digits)

by **SpAce** » Sat Jul 13, 2019 12:17 am

eleven wrote: The standard solution is an xy-chain
(1=73)r18c4 - (3=86)r8c76 - (6=1)r5c6 => -1r5c4,r1c6

I guess most if not all small BUG situations are solvable with XY-Chains (just like they're solvable with 3D Medusa). Has anyone tried to find the limits of that empirical result? In any case, I hate XY-Chains, so at the very least I'd try to masquerade it as something else

For example:

(17)r18c4 = (76)r8c86 - (6=1)r5c6 => -1 r1c6,r5c4

Or an Almost Hidden Quin (I'm not being serious):

(17)r18c4 = (7-6)r8c8 = (68437)r89471c6 => -1 r1c6

In some way you use it for the 3r9c7 case:

Code: Select all
(65==3)r9c4567 - r8c7 = (37-1)r81c4 = (16)r15c6 = > -6 r8c6; stte 8r8c6 = (8-3)r8c7 = (37-1)r81c4 = (16)r15c6 = > -6 r8c6; stte

In any case the BUG needs a shorter contradiction, which solves the puzzle. (like a UR, where the external candidates are a pair of the UR digits)

Good points. That's why I didn't think my BUG fulfilled Steve's "good" requirement, except for the nice start. When a DP solution is longer or clearly more complex than a normal one, and especially if it embeds a simpler solution, I consider it degenerate. It can still be fun and educational to use, though!

[Btw, see my yesterday's original BUG+8 solution for an example of a really degenerate one (the new one is that too, of course, but not so much). Even though it didn't make much sense, it was quite fun to try to find the simplest way to do it (not sure if I did). At first 6r4c8 seemed like the obvious target because it saw the most guardians directly, but that resulted in more complex chains and just as many of them too.]

So, is the BUG+3 basically useless here as well, or can someone find a more elegant use of it (for stte)? For practical purposes, I still think the nicest use of it is as a very simple two-stepper:

(56)r9c456 == (3)r9c7 => -5 r9c7 => BUG+1 => +6r9c6; stte

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