Grouped X-Cycles

Grouped X-Cycles extend X-Cycles by allowing grouped nodes - where multiple cells in a box-line intersection act as a single node. This enables stronger chains and more elimination opportunities.

Technique

1. Build a chain for a single digit using individual cells and grouped nodes.
2. A grouped node represents all occurrences of the digit in a box-line intersection.
3. Strong links connect a node to its conjugate; weak links connect nodes sharing a house.
4. Apply the same loop rules as X-Cycles: continuous loops eliminate; discontinuous loops force or eliminate.

Tips

• Grouped nodes represent 2-3 cells acting as one unit.
• The group is 'on' if any cell in it contains the digit.
• This is a natural extension of X-Cycles that handles more complex single-digit patterns.