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LinkedIn's Queen #564 (HARD difficulty) LinkedIn's Queen #564 (HARD difficulty)

I am watching the commentary of today's Queen puzzle (a 1* Star Battle puzzle), given that I complete it in about 2 minutes. But one thing I don't quite understand is his words

When one of these two has to be a queen, neither of these and neither of these can be a queen, since no two queens can touch each other (circled in black). That leave just one option in yellow (outside the black circle)

I rephrase the commentator's words in this way:

When a row containing a red square or yellow square (inside a black circle) (using his computer mouse to explain) is a queen, neither a red square above it and a yellow square below it can be a queen as no two queens can touch each other.

That leave just one option left for the yellow square (diagonally below a black circle).

How does he prove that the yellow square outside a black circle is a queen, given no obvious observation that it must be a queen?

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  • $\begingroup$ Can you expand on what squares the commentator is referring to? Your quote simply says these multiple times and it’s not clear what squares you are referring to. $\endgroup$ Commented Nov 15 at 12:17
  • $\begingroup$ What I am trying to say is the row containing black circle is commentator refers to. $\endgroup$ Commented Nov 15 at 12:44
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    $\begingroup$ I try my best to answer your question, @Pranay. $\endgroup$ Commented Nov 15 at 12:46

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More direct idea:

The bottommost unmarked cell in the light grey region eliminates every unmarked yellow cell - mark it.
This forces the light grey queen into row 3, which forces the blue queen into column 2, letting you place the red queen, followed by all the others.

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I believe the video explanation simply stepped over a bit of logic. While there is only one option left for yellow at this point, it's not as obvious as the video suggests.

If the top yellow was a queen, it would force the top right grey to be a queen and also force the red queen to be in the left red column, which leaves no option for a queen in the blue region.

I haven't found an easier explanation in the comments under the video as well, I suspect he simply knew the solution in advance to not cause any interruptions in the video and forgot this logic was required.

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The only way to solve this puzzle is looking at the region containing blue, green, gray, purple, orange, red and yellow, spanning from second row to fifth row. One thing I should ensure is the ratio of number of rows/columns and the ratio of the number of the colour regions must be the same.

Since there are four rows from the second row and the fifth row, that means I must pick four colour regions which suit in this region (blue, green, gray and red), which means I can immediately remove the yellow square inside the black circle right away. That is far better than his explanation.

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  • $\begingroup$ Why can you only pick red as the fourth color? $\endgroup$ Commented Nov 15 at 13:44
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Two adjacent eliminate side-neighbours

When you have two remaining in a group – row, column or colour – and they are adjacent to each other, they eliminate all immediate vertical and horizontal neighbours. This follows trivially from trying out both options.

Now, in this particular case, where do we go from there?

Note: the examples followed a different path than the tutorial, but the moves are valid for both

  • Rows 2, 7 have only two remaining, both in columns 2, 7.

    All others in columns 2, 7 eliminated

enter image description here

(Some intermediate steps that lead to the same position as the Tutorial are not shown)

  • Yellow eliminates one grey

enter image description here

  • Two adjacent remaining grey eliminate rest of row 3.

enter image description here

From there, a single blue remaining leads to a cascade that fills in all queens.

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