### ... by: Leren

This Nishio chain is also a Discontinuous Nice Loop type 3 - but for some reason your solver bypasses this AIC strategy. The solver's choice of Nishio chains also seems somewhat arbitrary - you could just as easily transfer the required contradiction to any of the cells in the loop. Also the graphic is a bit confusing - the 6 in G2 should be coloured green to highlight the contradiction in that cell (2 candidates both coloured green). Are there cases where Nishio chains are not also Nice loops?Andrew Stuart writes:

Correct on the connection with Discontinuous Nice Loop type 3. The green cell highlight I think is a carry over from previous strategies where I mark the end of the chain. Probably not necessary. The final candidate 6 in G2 is yellow as that follows the graphical convention of showing eliminations in yellow/red text. It would be green if it was part of the chain.

The solver returns the first instance of the strategy used but currently cant cycle through all instances of that strategy so I'm sure other formations of the same chain are possible as it's also a loop. I'd like to allow that in the solver and it's an upgrade I have in the job queue. There is a limit on the length of normal single chain AICs which I have to impose to stop the program taking too long to return (mainly for the grading feature which has to run through all the strategies). That means that some AICs might not be found and instead two chains in the double chain strategies like Nishio get to find the same result as each chain is under the limit. I've had several goes at optimising the AIC searchs but not to any great improvement in speed.

I haven't broadened Nishio to non loop type entities because the narrow definition I've worked with has start and end points on single candidates. But I'll be the first to admit there is overlap with other chaining strategies.

The solver returns the first instance of the strategy used but currently cant cycle through all instances of that strategy so I'm sure other formations of the same chain are possible as it's also a loop. I'd like to allow that in the solver and it's an upgrade I have in the job queue. There is a limit on the length of normal single chain AICs which I have to impose to stop the program taking too long to return (mainly for the grading feature which has to run through all the strategies). That means that some AICs might not be found and instead two chains in the double chain strategies like Nishio get to find the same result as each chain is under the limit. I've had several goes at optimising the AIC searchs but not to any great improvement in speed.

I haven't broadened Nishio to non loop type entities because the narrow definition I've worked with has start and end points on single candidates. But I'll be the first to admit there is overlap with other chaining strategies.