X-Cycle - Rule 2 (Odd number of links)
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 Weak Links (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 2 if it meets the following criteria:-
  • It contains an odd number of links.
  • There are no examples of consecutive weak links.
  • There is one example of an even number of consecutive strong links.
  • All other strong links occur in groups having an odd number of members.
This puzzle contains such a loop for candidates of value 5. If you examine the loop you will soon convince yourself of the truth of Rule 2 which states that the candidate at the first junction between two strong links must constitute a solution.