#236 Practising ALS-XZ Rule

[Gordon Hilton Fick]

I have been trying to use the mode 'Practising' with only the ALS-XZ Rule checked off. The counter with 'Create sudoku' goes past 50,000 with each attempt. I have been giving up by hitting 'cancel' but today I just let it continue and I got a puzzle after about a half an hour. I did not see how big the counter was.
'Practising' with XY-Chains gives a puzzle almost instantly.

[Bernhard Hobiger]

Try moving ALS-XZ up in the solver hierarchy (before XY-Chain)

[Gordon Hilton Fick]

Thanks. Your suggestion does give ALS-XZ instantly. Although, with this setting, most of the ALS-XZ steps are actually XY-Chains (I now have success finding XY-Chains). I then tried a hierarchy with XY-Chains ahead of ALS-XZ but then ALS-XZ ahead of Nice Loops/AIC and Grouped Nice Loops/AIC. This order still gives me ALS-XZ instantly and they are not XY-Chains. Fascinating. So with the default hierarchy, one (eventually) gets ALS-XS that are not AIC or Nice Loops. Perhaps these steps are somewhat rare(r).

[Bernhard Hobiger]

I see ALS-XZ as advanced technique, harder to find than simple chains, thats why ALS-XZ is rather late in the solver hierarchy. But as you noticed, every XY-Chain can be seen as ALS-XZ (a bivalue cell is an ALS, two weakly linked bivalue cells are two ALS with an RC). Every XY-Chain is of course a valid AIC as well, which means that every ALS-XZ consisting only of bivalue cells is also an AIC. These ambiguities are rather common.