daj95376 wrote:The XY-Chain in my first reply accounts for r8c3<>7.

Yes, but this discontinuous nice loop is more in keeping with your 2-digit POM analysis.

r8c3 -7- r8c4 =7= r7c4 =5= r7c1 -5- r1c1 =5= r1c2 =7= r1c3 -7- r8c3 ==> r8c3<>7

In case you remember little of NL notation , that's ... (7)r8c4 = (7-5)r7c4 = (5)r7c3 - (5)r1c1 = (5-7)r1c2 = (7)r1c3 ==> r8c3<>7

daj95376 wrote:That leaves this Kraken Row [r8] on <4> -- which is sufficient for r7c7,r9c6<>4.

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`(4-7)r8c2 = r8c4 - r7c4 = (7-4)r7c7`

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(4 )r8c3 - r5c3 = r5c7 - ( 4)r7c7

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(4 )r8c9 - ( 4)r7c7

That's as good as any ... and it only uses two digits. (I added the strong inference symbols for the kraken row.)

SudoQ wrote:My solver think that the fact that r7c6<>1 is a one-step solution, but I don't know if it is?

r7c6=4 is a "singles backdoor", so it's obviously a one-step solution. However, in keeping with the title of this thread, by what deductive technique can the exclusion r7c6<>1 be shown.