dxSudoku #65 Avoidable Rectangle Type 2

[@thomaswilke6312]

Very nice! I like your methodical presentation a lot. Extremely informative and precise. Thank you

[@dxsudokuchannel]

Glad it was helpful!

[@WindowsXP_YT]

1:48 Avoidable Rectangle (Type 2) If neither of these squares were 9, then the puzzle would have two solutions. Therefore, you can eliminate 9 from the rest of this column and block.

[@dxsudokuchannel]

Yes, this is the way the normal and avoidable Type 2 work. I go into more about the kill zone in the prerequisite video #46.

[@sandyhafenbrack141]

Thank you!

[@dxsudokuchannel]

:)

[@SmartHobbies]

“All unique rectangles have an avoidable rectangle variation”. Which do you have an easier time finding? I haven’t my eyes to spot the ARs yet but URs can be pretty easy when all candidates are showing by looking for the matching pairs in the 2x2x2.

[@dxsudokuchannel]

The ARs are pretty easy to find. The problem with them is they are very rare. Especially AR Type 2 is very rare. I don't think I've ever seen one in the wild. I just added the them to complete the set of 10 based on the Hodoku wiki page. For the URs I think Bug+1, Type 1, and Type 6 seem to be the most common. I have a really cool idea for generalized search algorithm I've been thinking about for a year. I may do something with at some point. You should watch the creating puzzles from scratch videos. There's some interesting insight into puzzle technique frequency you can conclude from the content.

[@dxsudokuchannel]

I like searching for the Type 6 ones because you look for sets of X-Wings.

[@dxsudokuchannel]

Hidden Rectangles seem to be pretty common too.

[@SmartHobbies]

@@dxsudokuchannel Thank you very much. I'll start looking for these in my puzzles.

[@sandyhafenbrack141]

Stupid question: Why wouldn't this technique work with given numbers?

[@dxsudokuchannel]

The stupid questions are the only kind I can answer! Sorry, one of my favorite sayings. So here's the problem with a given. Givens are carved in stoned. They cannot be moved. So there's no ambiguity in the cells making up the rectangle. Every puzzle has an initial set of givens. And every puzzle has a solution grid. The steps we take in solving the puzzle is called the solution path. Harder puzzles may have more than one solution path depending on the techniques we use. But the basic assumption we take in considering a puzzle to be valid is there is only one unique solution grid. There are sextillion number of solvable constellations of givens. Some constellations of givens have multiple solution paths and multiple solution grids. Most people consider the puzzles having multiples solution grids as invalid. Some people argue it the other way. I'm on the one-solution side of this argument because there are so many of both types we might as well just choose it to be the one way. So the proper phrasing and the way to think about the four values making up the Type 2 rectangle is this: We must assume we have only one solution grid. And if we have a solution grid where four values can be interchangeable this is not valid. We are generally assuming every constellation of givens we are solving has only one single solution grid. I hope my explanation makes this clearer. Here's a pretty good wiki page I use for reference on Sudoku uniqueness:hodoku.sourceforge.net/en/tech_ur.php My 10 tutorials on uniqueness techniques were based on this wiki page.