Hajime wrote:And the A&B method is called: 2-String Kite for candidate 1 and 4.

True, it's a Dual 2-String Kite. More commonly it would be called a Remote Pair, though.

In general, Remote Pairs are both Dual X-Chains (Kite is a short X-Chain) as well as Dual XY-Chains (with just the same two values in every cell). The Dual X-Chain view is simpler (better) because it's much more efficient in terms of links, digits, and candidates used, even though both use the same cells. The difference is easy to see:

Dual X-Chain (2x2 strong links, 2x1 digits, 2x4 candidates):

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`[(1)r9c4 = r5c4 - r4c5 = (1)r4c9] => -1 r9c9`

[(4)r9c4 = r5c4 - r4c5 = (4)r4c9] => -4 r9c9

Dual XY-Chain (2x4 strong links, 2x2 digits, 2x8 candidates):

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`[(1=4)r9c4 - (4=1)r5c4 - (1=4)r4c5 - (4=1)r4c9] => -1 r9c9`

[(4=1)r9c4 - (1=4)r5c4 - (4=1)r4c5 - (1=4)r4c9] => -4 r9c9

The strong links in the cells are superfluous, making the flip-flopping XY-Chains unnecessarily long and complex.

Note that both of those options need

two separate AICs to get both eliminations. Even some very experienced people have had the misconception that writing a Remote Pair as a single XY-Chain would somehow get both eliminations at once. That's not true at all. You need two different XY-Chains, just like you need two different X-Chains -- thus it's better to use the simpler X-Chains.

There's no easy way to write a Remote Pair as a single AIC to get both eliminations at once. Besides myself, not many people can do it correctly (or so I assume because I've never seen anyone else do it). In this case it's pretty simple ('.' in place of the standard '&' for better readability):

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`[1r9c4.4r4c9 = 1r5c4|4r4c5 - 1r4c5|4r5c4 = 1r4c9.4r9c4] => -14 r9c9`