What this pattern means
A symmetric grid is one that looks the same after a specific transformation. Reflection symmetry mirrors across an axis; rotational symmetry spins around a centre. The missing cell is whichever value makes the symmetry consistent.
How to spot it
- Visible cells form pairs across an axis (reflection) or orbits around the centre (rotation).
- The grid 'feels balanced' even though no single rule explains it cell by cell.
- Pairs of cells share orientations, colours, or fills that map under the symmetry.
Common visual signals
- Pair structure: every cell has a partner under the symmetry.
- Constant centre cells when the rotation is 4-fold and one fixed point exists.
- Diagonal stability when the symmetry's axis crosses the diagonal.
Step-by-step solving tactic
- 1Decide whether the symmetry is reflection or rotational.
- 2Identify the axis (for reflection) or order (for rotation).
- 3Map every visible cell to its symmetric partner.
- 4Apply the symmetry to derive the missing cell from its partner.
Worked examples from the bank
Common traps
- Treating reflection and rotational symmetry as interchangeable.
- Missing combined cases where two symmetries hold simultaneously (full dihedral).
- Reading the symmetry from only two cells — confirm with at least three pairs.
Practise symmetry questions
Items below are ordered easy → hard. Each links to the full question with explanation and distractor analysis.
- draft-reflection-refl-a05-2very easy
- symmetry-005very easy
- symmetry-009very easy
- draft-reflection-refl-a05-1easy
- draft-reflection-refl-a08-1easy
- draft-reflection-refl-a09-1easy
- draft-reflection-refl-a09-2easy
- draft-reflection-refl-a08-2medium
- filled-hollow-002medium
- filled-hollow-005medium
- filled-hollow-011medium
- gc-011medium
Related patterns
Apply this pattern under timed conditions
Take the free 10-question matrix reasoning practice test — every question carries the symmetry pattern or another commonly tested mechanic.