Rotational Symmetry Questions

The 3×3 grid is invariant under rotation — typically 180° (2-fold) or 90° (4-fold). Cells in the same rotational orbit carry the same content, transformed to match their position. The missing cell completes an orbit.

• Rotating the grid 180° (or 90°) lands every visible cell on another cell with matching content.
• Corner cells share an identity; edge cells share another; the centre is its own orbit.
• The rule operates on the grid's structure, not on a single attribute.

• Visible cells in corner pairs (0,0)↔(2,2) and (0,2)↔(2,0) share the same orientation up to rotation.
• Edge cells (0,1)↔(2,1) and (1,0)↔(1,2) form mirror pairs.
• Often combined with a colour or fill substitution for premium difficulty.

1. 1Identify the rotation order (2-fold vs 4-fold).
2. 2Map each visible cell to its orbit partner.
3. 3Apply the rotation to derive the missing cell from its orbit partner.
4. 4Check for a secondary attribute that also varies under the symmetry.

• Confusing rotational symmetry with reflection symmetry — rotation maps the grid onto itself by spinning, reflection by mirroring.
• Missing the rotation order — 2-fold and 4-fold look similar on small grids.
• Applying the rotation to only one attribute when several attributes participate.