Kakuro next step (Full Version)

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jordanbrown -> Kakuro next step (7/24/2022 6:51:59 PM)

What’s the next step? At this point the only strategy I know is to just try something and see if it works out, and that’s unsatisfying. Is there a logic step or pattern that I am missing?

[image]local://162780/D5A31ABC698C4419807DA6FE0D5C0E16.gif[/image]



hok0003 -> RE: Kakuro next step (7/30/2022 2:44:29 AM)

You'll have 9's in both of these columns, and therefore both rows.

[image]local://264849/9EA2E30176A04470BF135C16673D8E63.jpg[/image]



jordanbrown -> RE: Kakuro next step (7/30/2022 5:48:16 AM)

Thanks! I think that’s the first “2D” pattern I’ve learned. That got me a few more, but right now I’m stalled again. I’ll look some more before I ask for more help,



jordanbrown -> RE: Kakuro next step (7/30/2022 8:05:00 AM)

Got a few more off of your hint, plus one simple one I missed, but stalled again. Got another hint?

[image]local://162780/0A674668C3B945E7B3B68BB1BACFCB81.gif[/image]



hok0003 -> RE: Kakuro next step (7/31/2022 2:48:58 AM)

Honestly, I would use trial and error. But if you want to avoid that, here's something:

The squares marked in red add up to 45, based on the column clues.
The combined red and blue squares add up to 77, based on the row clues.
Therefore the 4 blue squares add up to 32, which greatly reduces their possibilities.

[image]local://264849/470520FF4CA04E0085D63EEEC3D44F15.jpg[/image]



jordanbrown -> RE: Kakuro next step (7/31/2022 5:04:11 AM)

Wow, that’s a level of analysis I would never have thought of. But I agree that just trying something and then backing out if it doesn’t work is probably easier. I just wanted to know it there were techniques I was missing before resorting to that.

Thanks!



jordanbrown -> RE: Kakuro next step (7/31/2022 5:15:55 AM)

But in this case the only way to get to 32 is 6899, and there is only one way to do that.



lopezmason -> RE: Kakuro next step (8/10/2022 6:29:21 AM)

WOW! It was unexpected. You guys are so talented. I still don't understand the whole mechanism of it. I really admire your intelligence. I will probably play and learn them from the basic and elementary level. Because looking at them is very interesting.
we become what we behold



jordanbrown -> RE: Kakuro next step (8/10/2022 6:39:19 AM)

I've only seen cases where I needed this level of analysis in the "very hard" puzzles.

Everything below that has yielded to lesser schemes, where you look only at one row (or column) and the columns (or rows) that intersect it.

Just eliminating marking only those options that are possible in both horizontal and vertical gets you a lot.
Then look for "this row needs a 3, and only one of these squares can provide a 3".
Look for "None of these squares has a 6, so the combinations that require a 6 are not possible".
Then "this row (or column) has two squares with {2,7}, so one of them must be a 2 and the other must be a 7, and no other square can have either a 2 or a 7". (Similarly for combinations of three numbers.)

And similar patterns.

The biggest secret is painstaking attention to detail. After the initial flurry of filling stuff in, I start walking across every single row and every single column, looking at all of the numbers and seeing how they relate to one another and to the possible options for that row or column. And every time I make a change, even one as small as removing the mark for a single value as not possible, that means that I have to reanalyze the crossing rows or columns.



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