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[immpy]

Hello all, enjoy the puzzle...

[Mogulmeister]

Another cracking puzzle Immp which made for quite a head scratching evening.

Looking around there was a Type 4 UR and one other (number ?) and some nice XY wing and even XYZ wing possibilities.

This is my single step solution after basics:

[Mogulmeister]

Another nice overlapping ALS XZ scenario.

Set A (violet) 2,5,6,7,9 plus green square (n-1 = 4)
Set B (brown) 2,6,8,9 plus green square (n-1 = 3)

Restricted common is 6.

Common candidate is 2 because that 2 in r7c5 (red) can see all the 2's in both sets so it can be removed. R7c5 <>2.

[immpy]

Thanks Mogulmeister. I like the way that ALS works. I am learning as you go through your examples of it. Will keep practicing for now.

cheers...immp

[Mogulmeister]

Absolutely Immp.

This took a little while but as with everything Sudoku - strong links.

[immpy]

Hey hey! Mogulmeister, I am getting the hang of this thing now. Common restricted candidate must be a strong link, yes? Then look for two ALS which share the common restricted candidate. Use n-1, where n is the number of candidates and -1 signifies the number of cells with those candidates. Any candidate common to both sets (other than the restricted candidate) becomes candidate Z. In any cell that sees all possible placements of Z in the two sets, Z can be eliminated. I have learned, and hopefully grasped something new today!! Thanks again Mogulmeister!

cheers...immp

[immpy]

As you remind us, everything in Sudoku is about STRONG LINKS! I am going to like using this a lot down the road.

[Mogulmeister]

Hi Immpy

Well done !

A tiny bit of fine tuning.

So in the ALS we have two main elements:

Restricted Common: This is a number that can only end up in one set or the other. In this case it is 6. It is eventually going to end up in either r2c5 or r8c5.

Yes it behaves like a strong link - the point is that the restricted common is always in a column or row with the same number in the opposite set. Be careful though - as you can see from one of the earlier ones that I did (below) that the locked common can sometimes have more than two occurrences . However remember that ultimately, the restricted common can only survive either in A or in B. Just like a strong link!

The common candidate as you say is a digit that sees all the other cells in both sets with the same value. If it does, it can be eliminated.

[Mogulmeister]

To illustrate look at this one from a few weeks ago with your new eyes:

[Mogulmeister]

So three 6’s in row six (two of them in A and one in B) but the 6 will only ever be in A (pink) or B (green). That’s the point.

[Mogulmeister]

In my experience this is much rarer but does happen. So long as the wider principle still applies you are good to go.

[immpy]

Indeed yes Mogulmeister. One of your earlier examples had the extra occurrence of the restricted common, but it still formed a strong link. Got it! The restricted common could also possibly be in the same box, not only same rows/columns, as I am sure you are aware. Common house is the key.

cheers...immp

[Mogulmeister]

Thanks Immp - quite right. House.