X-Cycles are similar to Singles Chains in their use of links between similarly numbered candidates within a unit (row, column or box).
Links are classed as Strong Links
(dark green) if the candidates they connect are the only two of that value in the unit, or
(light green) if there are additional candidates of the same value within the unit. A group of such links becomes an
X-Cycle if they join together to form a complete loop. An X-Cycle is subject to Rule 1 if it meets the following criteria:-
It contains an even number of links.There are no examples of consecutive weak links.Consecutive strong links are
acceptable provided they occur in groups having an odd number of members.
The present puzzle contains such a loop for candidates of
value 9. If you examine the loop you will soon convince yourself that either all of the red candidates are solutions, or all of the green
candidates are solutions. Either way the units highlighted in blue will have their requirement for a 9 solution satisfied. Rule 1 states
that additional candidates in weak link units may be removed