Empty Rectangle and the LOGIC Behind It

[@thejose965]

Great lucid explanation... Thanks a ton from Kuwait 🙏

[@a_son_of_light]

I was so stuck...all that was left in the puzzle were pairs, triplets, quads, quints, septs in every direction and within all blocks...nothing to eliminate! Also no x-wings, x-y wings, xyz wings, w-wings, and no skyscrapers that could eliminate any little number. Then I happened upon this video. Thank you so much for the perfect explanation....one empty rectangle solved the puzzle completely. I have to start always looking for empty rectangles in every puzzle I do so that I will always have it in my arsenal of techniques.

[@tomdalziel4607]

Thank you for taking the time to explain every step of the process so clearly!!! 😀💟

[@charlottewebb3364]

I Like your nuts and bolts approach in describing these patterns. You should write a book or make one available for download. It would be well worth the purchase.

[@JB23669]

This is so confusing. Thank you so much for trying to explain this but I’m just having a hard time finding these patterns

[@michelemoneywell8765]

It might be easier to find the conjugate pair first. Is the pair in the same row, as at 6:40. Then look down the column of each point for an empty rectangle. Is conjugate pair in the same column (last example)? Then look at the row for each point to see if it an empty rectangle exists. Once you have a qualifying conjugate pair and empty rectangle, label the points x and y. See where the y row/column intersects the leg of the empty rectangle column/row. Voila, you may have eliminated a choice, and that elimination may make solving easier.

[@Judith34816]

She stops explaining what is meant by "one row and one column" at 5:10.

[@michelemoneywell8765]

Thank you, skipped ahead. 5 minutes 10 seconds to explain one row, one column was too much.

[@jenschafer269]

This helped me finish the NYT hard puzzle today!

[@wegtennis8740]

In your last example, isn't there also an empty rectangle related to the 2's in block 9 that would lead to the elimination of 2 in the lower left corner of block 3 (cell 7)? This would then leave 2's in cells 3 and 9 of block 3, resulting in the same final result of eliminating the 2 in cell 6 of block 9? Would one of you smart folks let me know if I'm understanding the process? Thx

[@noney81]

Saw that too and think it works. With the empty rectangle in the video the 2 is restricted to column 7 in box 9 so that eliminates the 2 from box 3 in that column as well. Works both ways for both boxes.

[@samantajansch1669]

Thank you so much for this long explanation, finally I got it! Greetings from Germany!

[@a_son_of_light]

Problem is to remember to look for it the next time we're stuck! 😊😊

[@wwfgumby]

Well described, thanks.

[@RealGrover]

The first example was at first very frustrating to me because I couldn’t find any use in the excluded 3. There‘s just no follow-up. But it made me look very closely until I managed to spot my very first xy wing 🎉🎉🎉 Hurray! There‘s one with the pivot in R3,C9, x in R3,C3 and y in R9,C9. It conveniently excludes the 2 in R9,C3 and the whole puzzle unravels easily, even disregarding the empty rectangle trick. So, while it was an underwhelming empty rectangle it would make an excellent example for a super helpful xy wing 😅 Thank you!

[@duffelesser6210]

Amazing! thx from germany!

[@vidyanandsinha8879]

Thanks

[@eugenetswong]

Thanks for this! I didn't use it specifically, but it didn't help. Using a conjugate pair like that makes a big difference.

[@kaskazimnoch9583]

You're the best.

[@jaimeriquelme6727]

Smart girl, thanks for your lesson and your time.

[@thomaswilke6312]

Very clear and concise explanation. Thank you very much

[@kyldare]

I'm having a hard time figuring out which number is considered to be in the same row/column. As an example, why couldnt the 2 on h9 be considered the one on the same column then removing the 2 from C6 instead? For the example on 12:53

[@Jake_Cotumaccio]

If you start by choosing the 2 on H9, you’d need there to be only one other 2 in row 9. This is what she means by “conjugate pair”- there’s only two instances of a given digit (2 in this case) in a particular row or column. However, because there are more than two 2s in row H, you can’t use the 2 on H9 as the basis for the empty rectangle trick. You can use the 2 in column 6 because there are only two 2s in that column, meaning it is part of a conjugate pair. Hope that helps!

[@michelemoneywell8765]

A conjugate pair (only two possibilities in a row or column) and an empty rectangle (one row and one column in a block where a digit can go) are needed for the trick. Row H does not contain a conjugate pair. Column 6 does.

[@kathimeci5179]

WOW! Very complex. Not the explanation, but the theory. Makes me think I should stick with crosswords.🤣

[@steven-ky2ps]

After watching this I realize how dumb I am. LOL

[@freshfreenlovinit]

This lady is a born teacher.

[@VistasdelMar2008]

In your last real world example, does the logic of eliminating the 2 in the 9th column also imply that the 2 in the same row immediately adjacent in column 7 also get eliminated ?

[@aspartaami]

No, because it doesn't see the empty rectangle. Only the one seeing the empty rectangle can be eliminated.

[@michelemoneywell8765]

Another explanation of the "no" answer: an empty rectangle has a row and a column in the same block. The eliminated choice (only one, let's call it "e") has to be in the same row or same column as the empty rectangle. If the "x" is in line with a row, then the "e" is in line with the "y" row and empty rectangle column. If the "x" is in line with a column, then the "e" is in line with the empty rectangle row and "y" column.

[@seemashrivastava1661]

Is it necessary that the conjugate pair should be in different blocks,Or they can be in same block?

[@macfid]

Go to 6:40

[@zattopekk]

A pair (same numbers!) in ONE block?????

[@michelemoneywell8765]

Different blocks. If x is in line with an empty rectangle (er) column, then want to eliminate intersection of er row and y (column). (6:40) If x is in line with an er row, then want to eliminate intersection of er column and y (row). You would not get that intersection if x and y were in the same block.

[@dunnetahl]

Really aweome technique. Just used this with multiple numbers to solve a puzzle I had completed all pairs, triplets, then x wing, y wing, swordfish and slanted skyscrapper were all nil, but I had several key empty rectangles that helped me solve the puzzle. This technique is really easy to spot, understand and apply.

[@yolotaylor993]

Very clear, thanks

[@nouraalwani1245]

I think that your explanation for calling this method an empty rectangle is wrong. The empty rectangle refers to the area that consists of the block , the conjugate pair, and the cell that has the number that would be eliminated. When you connect all these they create a rectangle shape.

[@TomJones-tx7pb]

If you have a valid puzzle, you can switch rows with columns and produce another valid puzzle. If you have a valid puzzle you can switch 2 rows in the same block and produce another valid puzzle. Once you know these 2 concepts, you do not need to belabor all the different patterns for a solving technique.

[@billgillaspey9036]

I'm really enjoying your Sudoku videos; thank you for them. Question: who determines--and/or HOW do they determine--whether a puzzle is hard or "easy". I'm assuming that the number of slots out of 81 slots which are blank is one factor. But what else: is it part of the algorithm that generates these puzzles? Is there Sudoku "checker" that rates them (like a restaurant reviewer...) . Always wondered....

[@Sir_Amnesia]

Jesus you went on a bit

[@andremenard2933]

Videos way too long, she repeats too much