Matrix and Pattern Completion
About 7 min · Logical Reasoning · English
Time worked out from the lesson's 548 words at 150 words a minute, plus a minute for each question.
Matrix and Pattern Completion is a visual reasoning topic in SOF IMO's Logical Reasoning section. Questions present a 3×3 grid (or occasionally 2×2 or 4×4) with one cell missing, and you must identify which option correctly completes the pattern. Some problems use repeating sequences of figures, numbers, or symbols instead of grids.
Key ideas
- Grid-based logic: In 3×3 matrices, the pattern typically operates row-wise (all rows follow the same rule), column-wise (all columns follow the same rule), or both. Always check complete rows and columns first before analyzing diagonals.
- Figure transformation rules: Elements may rotate (90°, 180°, clockwise/anticlockwise), flip horizontally or vertically, increase/decrease in size, change shading (white → gray → black), or add/remove internal features like dots, lines, or corners.
- Element progression: Shapes may cycle through a sequence (circle → square → triangle → circle), positions may shift systematically (top-left → center → bottom-right), or the number of elements may follow arithmetic patterns (+1, +2, or ×2 per cell).
- Combined operations: A single cell may result from combining features of other cells in the same row or column. Example: Cell 3 = union of shapes from Cell 1 and Cell 2, or Cell 3 contains only features common to both Cell 1 and Cell 2.
- Number and symbol patterns: When matrices contain numbers or symbols, apply arithmetic operations (addition, subtraction, multiplication across rows/columns) or look for differences, ratios, or modular patterns.
Watch out for
- Checking only rows, ignoring columns → Always verify the pattern holds both row-wise AND column-wise. Many students find a row pattern and stop, missing a conflicting column rule that actually governs the missing cell.
- Assuming the first rule you spot is correct → Test your hypothesis on ALL complete rows/columns. A rule that works for Row 1 but breaks in Row 2 is wrong. The correct rule must apply uniformly across the entire matrix.
- Overlooking combined operations → If no single rule works, the missing cell might combine two elements (union, intersection, subtraction of features). Students often miss this and force a single-transformation rule that doesn't fit.
Quick reference
- Systematic scan order: Rows → Columns → Diagonals → Element features (count, color, orientation).
- Most common rules: Rotation (90°, 180°), arithmetic operations (addition, subtraction), feature addition (union/intersection), and cyclic progression (shape sequences).
- Time-saving tip: Eliminate obviously wrong options first — if Row 1 and Row 2 have only triangles and circles, a square in the answer for Row 3 is likely wrong.
- For number matrices: Check if sum, difference, product, or ratio of two cells equals the third. Test all three possibilities quickly.
- If stuck after 45 seconds: Mark your best guess from remaining options and move on. Don't spend 2+ minutes on a 1-mark question.
Check yourself: 3 questions
1. In the following 3×3 matrix, each row follows a specific pattern. Find the missing number that should replace the question mark. Row 1: 2, 4, 8 Row 2: 3, 6, 12 Row 3: 5, 10, ?
2. Complete the following 3×3 matrix by finding the pattern. What number should replace the question mark? Row 1: 7, 10, 13 Row 2: 11, 14, 17 Row 3: 15, 18, ?
3. Complete the matrix pattern: Row 1: 2, 4, 8 Row 2: 3, 6, 12 Row 3: 5, 10, ? What number should replace the question mark?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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