Grouped x-cycle is equivalent to grouped colouring (Double Dragon) as described here.

Due to its simplicity, like xy-chain and x-cycle, grouped x-cycle is a subset of nice loops that can be identified without the need of a bilocation/bivalue plot.

In a grouped x-cycle, nice loop propagation always follows alternate links with 'strong inference' and 'weak inference' (refer definitions of 'link', 'strong link', 'strong inference' and 'weak inference' here). A link with strong inference or weak inference can enter or leave a grouped node (ie. a node made up of 2 to 3 cells) in a box, eg.

......[node A]-x-[node B]=x=[node C]-x-[node D]=x=[node E]-x-[node F]=x=[node G]-x-[code H].........

where:

[node] = [cell 1] or [cell 1|cell 2] or [cell 1|cell 2|cell 3]

the notation '=x=' is a link with strong inference (+ve label)

the notation '-x-' is a a link with weak inference (-ve label)

In a grouped x-cycle nice loop, if the links propagate alternately in a cyclic manner (ie. no adjacent links are of same type), the loop is said to be 'continuous'.

With continuous grouped x-cycle, candidates can be eliminated outside the loop but within the unit of the links with weak inference (broken lines) as demonstrated below:

A 'discontinuous' x-cycle nice loop has exactly one discontinuity at 2 adjacent links of the same type (ie. both links with strong inference (solid lines) or both links with weak inference(broken line). Nice loop notation for a discontinuous nice loop always starts from the discontinuity.

If the adjacent links are links wih strong inference (solid lines), a candidate can be fixed in the node at the discontinuity, as demonstrated below:

If the adjacent links are links with weak inference (broken links), a candidate can be eliminated from the node at the discontinuity, as demonstrated below:

Nice loop notation:

example 1: [r5c9]-5-[r8c9]=5=[r8c4]-5-[r4c4|r5c4|r6c4]=5=[r5c6]-5-[r5c9] => r5c9<>5

example 2: =[r1c1]-3-[r9c1]=3=[r7c3]-3-[r5c3]=3=[r5c9]-3-[r1c9]=3=[r3c7|r3c8]-3-[r3c2]=3=[r1c1]-

example 3a: [r2c9]=9=[r2c3]-9-[r5c3|r6c3]=9=[r4c1](-9-[r4c9])-9-[r8c1]=9=[r8c7]-9-[r7c9|(r4c9)]=9=[r2c9] => r2c9=9

example 3b: [r7c9]-9-[r2c9]=9=[r2c3]-9-[r5c3|r6c3]=9=[r4c1]-9-[r8c1]=9=[r8c7]-9-[r7c9] => r7c9<>9

In example 3a, candidate '9' appears exactly 3 times in column 9. The expression (-9-[r4c9]) shown in blue is a multiple inference that enables the link [r7c9|(r4c9)]=9=[r2c9] to be treated as a link with strong inference, thus the placement of the '9' in [r2c9].