The New Sudoku Players' Forum

[Mauriès Robert]

Hi,
At what level of difficulty do you place this puzzle and how do you solve it ?
9..6....3....43....547...2..48...7..7.......2..9...38..1...729....19....6....2..5

Hidden Text: Show

Robert

[champagne]

rated 9.0 by skfr,

middle range but it can be a boring solution
9.0 is just in the mood of your process.

[SpAce]

At what level of difficulty do you place this puzzle and how do you solve it ?

Easy with coloring, if you don't care about documenting the moves. Took me three coloring rounds (using just basics): 2b2, 2r4, 7s.

[eleven]

If you allow to eliminate 2r4c5 by contradiction with (many) singles and a locked candidate, it can be solved with techniques usually used here, e.g. by eliminating 6r6c69 and 5r7c3.

[Mauriès Robert]

Hi SpAce,

Easy with coloring, if you don't care about documenting the moves. Took me three coloring rounds (using just basics): 2b2, 2r4, 7s.

I would be interested to see in detail your resolution with GEM, to better understand GEM. Is that possible?
Thank you.
Robert

[SpAce]

Hi Robert,

I would be interested to see in detail your resolution with GEM, to better understand GEM. Is that possible?

Sure, I saved the images:

gem_2b2: Show

Screen Shot 2019-11-15 at 14.37.18.png (84.46 KiB) Viewed 613 times

(2)b2p24 => -158 r1c5

gem_2r4: Show

Screen Shot 2019-11-15 at 15.07.10.png (87.08 KiB) Viewed 613 times

(2)r4c4 -> (empty)r4c9 => -2 r4c4

gem_7r9: Show

Screen Shot 2019-11-15 at 15.33.11.png (80.6 KiB) Viewed 613 times

(7)r9c38 => -458 r8c6; stte

--
(I make no guarantees that there aren't mistakes.)

[eleven]

The first image eliminiates the 2r4c5 exactly as by just trying it.

What i want to say is, that in harder puzzles these methods often effectively are (maybe nested) contradiction nets, and the alternative part is just a fig leave to hide it.

[SpAce]

The first image eliminiates the 2r4c5 exactly as by just trying it.

What i want to say is, that in harder puzzles these methods often effectively are (maybe nested) contradiction nets, and the alternative part is just a fig leave to hide it.

That's absolutely correct. As can be seen in the image, the Light Side parity didn't propagate at all, so it was effectively the same as trying 2r2c4 or 2r4c5 directly.

One slight difference, though. If it hadn't produced the placement of 2r1c5, we'd still gotten a single trap elimination -2r1c2. That's the main point of doing a binary coloring in the first place. The primary goal shouldn't be finding a contradiction that solves the coloring, even though it's usually the most effective result. The goal should be finding those pincering eliminations where both branches agree. It's more fun and elegant, I think, and they're somewhat easier to document too. If you do find a contradiction, it should be considered a lucky side-effect. That way it doesn't stink of T&E so much. In fact, I have mixed feelings if I do find that contradiction because it means all those nice trap eliminations found earlier are wasted (because the contradiction gets them too).

That idea can be seen more clearly in the second coloring, even though it's pretty lopsided too. Without the contradiction we'd still gotten the +6r6c2 (like in your suggested solution) and all its cascading placements. All the contradiction gave us additionally was +2r4c1,r6c4 (difference in SE: 7.2 vs 6.9). In the third coloring it's even clearer, as it produced a bunch of loops (hence the tons of newly minted par-candidates) and eliminations around the grid. It's a more balanced coloring anyway, which I guess reflects that the puzzle was much easier at that point (SE: 9.0 -> 8.4 -> 6.9 -> end).

That said, I think you're quite right in general. In harder puzzles a normal binary coloring may not produce much, so it may effectively turn into a SIN (Single Implication Network; i.e. Nishio or T&E) -- if you're lucky. In fact, spotting those candidates where even a SIN can work (without nesting) might be difficult in those cases, as they're not necessarily ones you'd think of attacking (no strong links). Either way, that's pretty much T&E so it's not a very satisfying way of solving. In the worst case a long-winding coloring ends up with the solution and no contradiction, so it's been a total waste of time for someone like me who discards such accidental backdoor solutions (no different from guessing).

[Mauriès Robert]

Hi Eleven and SpAce

The first image eliminiates the 2r4c5 exactly as by just trying it.
What i want to say is, that in harder puzzles these methods often effectively are (maybe nested) contradiction nets, and the alternative part is just a fig leave to hide it.

I agree with you on this point.
I try to understand the GEM technique, and I admit that I have trouble finding my way around in all these colours. But I understand the principle.

I still give you my resolution with TDP.

A first set of conjugated tracks is formed with P(4r5c78) and P(4r6C9) => -4r6c4 (it is equivalent to a Finned Swordfich).

A second set of conjugated tracks is formed with P(2r4c1) and P(2r4c45)=P(2r4c4)∩P(2r4c5), because it is true that this group of candidates is promising.
We obtain (see figure1 below) that P(2r4c1)∩P(2r4c45) ={6r6c2, 3r5c2, 6r2c3, ...} solution and eliminations, but also many candidates of P(2r4c45)=P(2r4c4)∩P(2r4c5) are identified which will then be colored in a single color (yellow).

Hidden Text: Show

We then see by completing the yellow track (figure 2) that we can eliminate 158r1c5 so that 2r1c5 is solution and with it all the candidates of P(2r4c1). But it also means that the yellow track is invalid (contradiction in block 2)

Hidden Text: Show

Then, the puzzle easily ends with another set of conjugated tracks, for example with P(5r7c3) and P(3r7c3) which gives
P(5r7c3)∩P(3r7c3)={7r9c3, ...} solution and end.
But here again we see that P(5r7c3) is invalid (contradiction in r1c3).

Hidden Text: Show

Sincerely
Robert

[eleven]

So we have 3 ways now to place 2r1c5 and it's a matter of taste, which one to prefer.

I agree with SpAce and I really don't want to spoil your fun finding GEM/TDP solutions for puzzles, which otherwise need more brute attacks. However they are not the majority.