Grouped X-Cycles

Level 11 · Red Belt

Strategy:

Single-Digit Chains

Requires:

X-Cycles

Overview

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.

How It Works

  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.

Example

Look for Grouped X-Cycles.

1

Grouped X-Cycles

Found a Grouped X-Cycle on digit 1.

2

Grouped X-Cycles

Two weak links meet at the same group — this group must contain the digit.

3

Grouped X-Cycles

The cycle has 5 grouped nodes. The determined group is at [r2c4, r3c4].

4

Grouped X-Cycles

Digit 1 must be in group [r2c4, r3c4]. If the group is a single cell, place 1 there; otherwise eliminate 1 from cells seeing all group members.

5

Grouped X-Cycles

Apply the consequence for group [r2c4, r3c4]: place 1 if it is a single cell, otherwise remove 1 from the highlighted peers.

6

Result after applying the technique.

Tips & Patterns

  • 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.