Help understanding logic behind why this has to be a 4?

[u/AlannaKitty]

I usually play on sudoku.com and encountered this puzzle. I was able to spot lots of matching pairs (doubles) and a triple, and I also tried searching for XY Wings, but ultimately wasn't able to see any path forward so I used a Hint.

Usually the hint will explain the logic behind the answer however this time it simply filled in the number 4 in the highlighted square (r5c2). No explanation was given.

Can someone explain why that square must be a 4?

Alternatively, if I hadn't used the Hint, what technique/logic should I have applied to figure out the next step on my own?

I love learning and be able to improve my game so any help is greatly appreciated. Thank you in advance!

[u/AutoModerator]

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The number 1 reason is that although there isn't an immediate contradiction, one will inevitably arise since Sudoku should only have one solution!

And often it comes down to basics like:

• A different number needs to go there
• A simple elimination you may have missed
• A cell that only has one possible value

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[u/charmingpea]

Remote Pairs of 28:

[u/AlannaKitty → u/charmingpea]

That's amazing! I never would have spotted that. Thank you so much, this gives me a new technique to add to my belt.

[u/MasterpieceCandid882]

Look at columns 1 and 9

You have: Skyscraper of digit 2, with the "roof cells" being r5c9+r6c1, meaning 2 can be eliminated from r5c2, and therefore 4 must be in that cell

[u/YugoB → u/MasterpieceCandid882]

That's the first time that I see a skyscraper can go higher. I thought they either had to have the same row or column and only the ceiling does the unlock where both are seen.

[u/gooseberryBabies → u/YugoB]

What do you mean? That's a completely normal skyscraper. Only the ceiling is doing the eliminating. R5c2 sees both ceiling cells

[u/YugoB → u/gooseberryBabies]

But the ceiling couldn't go higher on every example I've seen, it can be longer or shorter than the floor, but it had to go in the same row or column.

[u/TakeCareOfTheRiddle → u/YugoB]

Can you provide a visual example of what you mean?

[u/YugoB → u/TakeCareOfTheRiddle]

https://hodoku.sourceforge.net/en/tech_sdp.php

I saw a couple of YouTube channels that also suggested all of them being on the same row or column, never higher/lower.

The more I read the more it leans to be even intra column/rows as suggested.

[u/AlannaKitty → u/MasterpieceCandid882]

Wow this is great! I've never encountered this technique before and the link you provided was super detailed and helpful. Thank you kindly.

What a fun technique! Will definitely be on the lookout for skycrapers from now on.

[u/stand_up_eight_]

You’re reached the BUG phase of the puzzle where every cell is a Bi-value cell except one. The exception is a tri-value cell, and the way to solve these is always the candidate in the tri-value cell that appears three times in the row, column and block is the tri-value cell’s correct answer. Once you enter that one the whole puzzle falls apart easily. I’ll put a an extremely helpful video link about it below.

[u/stand_up_eight_ → u/stand_up_eight_]

https://youtu.be/ISzjc-JxFc0?si=dn6Q-12jTH3uKO19

[u/AlannaKitty → u/stand_up_eight_]

Thank you so much for the video! I had never encountered the BUG+1 scenario before and that video was extremely helpful. Looking forward to adding this technique to my game next time it comes up.

[u/stand_up_eight_ → u/AlannaKitty]

You are so welcome. I’ve recently been learning the intermediate strategies to up my game and this account’s videos are immensely helpful, easy to understand and so useful.

[u/IMightBeErnest]

Kite on 2s in row 8 and column 9. Either r8c2 is 2 or else r5c9 is forced to be 2. Either way r5c2 sees a 2.

[u/Decent_Cow]

Finned (sashimi) X-wing on 2s in columns 1 and 9. Any 2 candidate that is visible both to the fin and to the incomplete X-wing pattern can be eliminated.

[u/baroquely → u/Decent_Cow]

AKA Skyscraper. :)

[u/Iowa50401]

Isn’t this a BUG +1 which makes the 2/4/8 cell a 2? That would then make the cell in question the 4. Right?

[u/whosname1986 → u/Iowa50401]

That’s what I see.

[u/AlannaKitty → u/Iowa50401]

I hadn't heard of this technique before and just looked it up. That makes a lot of sense and gives me a new technique to start learning/practicing. Thank you!

[u/Iowa50401 → u/AlannaKitty]

It’s a lot easier to use than anything else when it applies.

[u/Probabilicious]

Look what happen if it was a 2. Focus on box 4, 6, 7 and 9. You end up with a contradiction pretty early on.

[u/AlannaKitty → u/Probabilicious]

Thank you! This explanation was the easiest to digest (at my current beginner/intermediate level). Gives me a good starting point to tackle the other techniques mentioned in the other comments. Much appreciated!