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Hi, Paladin! Haven't heard from you in quite a while.

You've reached a valid conclusion, but I can't quite follow your logic. Here's the problem.

r1c4 (+) --> r1c5 --> r7c5 --> r9c6 --> ...

Hi, George!

We'll have to ask SamGJ to weigh in here about adding new techniques. I don't think you need to use anything beyond X-Wings to solve his puzzles, yet, but I'm not certain.

On the puzzle ...

Hi, Kowloon!

I'm not certain I understand your question, but maybe this is what you're asking about.
46+ . . . . . * . .
. . . . . . . . ...

Hi, Kathy!

If you look closely you'll find a "hidden pair" {4, 5} in column 3 -- specifically, in r2c3 and r8c3. So the only spot in row 2 where the "9" can possibly fit is at r2c4.

Oh -- I often fi ...

I've always thought of a constellation as an XY-chain (bivalue cells only) but this one passes through a cell that is solved (r7c6) and one that has 3 candidates (r5c8). Am also wondering if the 'alph ...

That's a very nice analysis, Matt. I particularly like the way you noticed how the two "X-Wings" intersect each other ... I missed that entirely, although I did find the same "anomaly" when I worked t ...

Hello, Blackwood!

The short answer is that you have an "X-Wing" formation in columns 1 and 6, on digit 7. In other words, since there are only two places to fit a "7" in column 1 (at r6c1 or r9c1) an ...

Hi, wfbeach!

I don't think there are two solutions. Maybe you noticed the same thing Louise56 was worried about ... check out [url=http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=1541]this p ...

"A rose by any other name would smell as sweet."
The original description/method of nishio is the following: For a grid focused on a single digit. Assume that digit occupies a certain start cell. If, ...

Hi, Jake! Thanks for writing back. And thanks for the diagram. Specific examples are easier to follow than abstract explanations.
1xx|x1x|xx1
xxx|x1x|xx1
1xx|x11|1xx
-----------
xxx|xxx|xxx
xxx|x11|1x ...

Wow! We have a very good discussion going this time. Thanks for posting this puzzle, Keith.
The original name for the "empty rectangle" was "hinge", which I think is more descriptive. You will find mo ...

... but there might be a more sophisticated solution which eludes me.
At this point in the puzzle there are a couple of "Nishio" moves that will solve it.
*------------------------------------------- ...

Hi, Jake!

I'm a little confused by your post. Are you asking abou the "X-Wing" pattern? Or about the "XY-Wing"? Since you mentioned a rectangle, I suppose you're asking about the "X-Wing".

The first ...

Did you note the squirmbag (so called per Marty above -- a five-level x-wing I think) on the 2s removing the 2 from the {127} in r9c2 and leaving a bivalue cell. I am trying like heck to make that cri ...

Hi, Matt!

You're right -- I did have to depend on a "finned swordfish" to eliminate the "5" at r2c5. And having a pair in that cell is essential to the forcing chains I found. I guess the "finned swo ...

Here's how I solved this puzzle. The first time through I concentrated on r4c5; going over it again, I noticed that it's easier to work from r5c2. Basic stuff got me here.
*--------------------------- ...

Hi, Matt!

I did solve this puzzle by concentrating on two "double-implication chains". The first one started from r4c5, and the second one (later) started from r6c5. I'll have to reconstruct it befor ...

Hi, Dan!

That's not a sudoku puzzle. It sounds like a magic square.

Clearly if it's a 3x3 square it's impossible. Since the sum of the digits 1 - 9 is 45, and every digit would be included in two su ...

Hi, Jeff!

I'm not sure I understand your question, but I'll give the best answer I can.

The only way to "solve" a cell in a sudoku puzzle is to reduce it to the status of either a hidden single or a ...

Hi, Pete!

The hint relies on "line/box interaction".

The "3" in the lower right 3x3 box must lie in column 7. Therefore there cannot be a "3" at r1c7, leaving "2" as the sole candidate. dcb