Figure Matrix and Missing Figure: Row and Column Rules, Number Matrices and Completion Questions for SSC Non-Verbal Reasoning

In a figure matrix question, a grid of figures (usually 3 × 3) is given with one cell blank, and you must pick the figure that completes the pattern. A related type is the number matrix, where a number is missing. This guide on figure matrix and missing figure for SSC explains the row-wise and column-wise rules, the operations on symbols and the rules for number matrices, with solved examples, practice questions and FAQs.

Method for the Figure Matrix

1. Check the rule in the first row; confirm it with the second row.
2. If the rows do not show a pattern, check the columns.
3. Check the rule for the diagonals or for the first two figures giving the third.
4. Apply the rule to the third row (or column) and find the missing figure.
5. Use elimination among the options.

Common Rules in a Figure Matrix

Number Matrices

In a number matrix, numbers are arranged in rows or columns, and one is missing. Find the rule from the complete rows or columns.

Solved Examples

Example 1 (symbol addition). In each row, the third figure has all the symbols of the first two. If the first two figures of the third row have a circle and a square respectively, what is the missing figure?
The figure with both the circle and the square.

Example 2 (cancellation). In each row the third figure has only the symbols that are not common to the first two. The first figure of the last row has a circle and a line and the second has a line and a dot. What is the third?
The common symbol is the line, which cancels. The third has the circle and the dot.

Example 3 (number matrix). Rows: 2, 3, 6; 4, 5, 20; 6, 7, ?
The rule is the product of the first two: 6 × 7 = 42.

Example 4 (number matrix). Rows: 4, 9, 13; 6, 8, 14; 7, 5, ?
The rule is the sum of the first two: 7 + 5 = 12.

Example 5 (constant sum). Rows: 8, 1, 6; 3, 5, 7; 4, 9, ?
Each row adds up to 15: 15 − 4 − 9 = 2.

Example 6 (square pattern). Rows: 2, 4, 16; 3, 9, 81; 4, 16, ?
The second is the square of the first and the third is the square of the second: 16² = 256.

Tips and Tricks

• Find the rule using the first two rows and verify it using the last complete row.
• If the numbers seem to follow no rule in the rows, check the columns and the diagonals.
• For the symbol matrices, list the symbols of each figure and apply the rule on the lists.
• Check the Latin square rule (each row and column has each figure once) first if the figures are only three types.
• Always check the sum, the product, the difference and the squares in the number matrices.

Quick Tips

• Use the complete rows to find the rule.
• Check the columns if the rows give no pattern.
• List the symbols of the figures to apply addition or cancellation.
• Check the sum, the product, the squares and the difference in number matrices.

Quick Revision Points

• A Latin square has each figure once in every row and column.
• Symbol addition combines the symbols; cancellation removes the common ones.
• Number rules: sum, product, difference, square.
• Verify the rule on a second row.
• Eliminate the options that break the rule.

Practice Questions With Answers

1. Rows: 3, 4, 7; 5, 6, 11; 8, 9, ?
   Answer: 17
2. Rows: 2, 5, 10; 3, 4, 12; 4, 6, ?
   Answer: 24
3. Rows: 5, 2, 3; 9, 4, 5; 12, 7, ?
   Answer: 5
4. Rows: 1, 8, 27; 2, 16, 54? What type of rule is it?
   Answer: Check the rule on the complete rows to decide
5. Rows: 6, 7, 8; 9, 10, 11; 12, 13, ?
   Answer: 14
6. If the row sums are all 18 and a row has 7, 5, ?, find ?
   Answer: 6
7. Rows: 2, 4, 16; 5, 25, ?
   Answer: 625
8. What rule is applied if the common symbols of the first two figures cancel in the third?
   Answer: Cancellation
9. What do you check if the row rule is unclear?
   Answer: The columns and the diagonals
10. What is a Latin square arrangement?
    Answer: Each figure appears once in every row and column

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Non Verbal Reasoning notes page, read the previous topic Figure Analogy and Classification and the next topic Pattern Completion and Incomplete Figures.

Frequently Asked Questions

What is a figure matrix?

A grid of figures with one missing cell that must be completed using the rule of the pattern.

How do I find the rule?

Compare the rows (or columns) and see how the third figure is related to the first two.

What is symbol cancellation?

Removing the symbols that are common to the first two figures.

What is a number matrix?

A grid of numbers with a missing number which follows a row or column rule.

What are the common rules in a number matrix?

Sum, product, difference and squares.

What if the rows have no pattern?

Check the columns and the diagonals.

Is this topic asked in SSC?

Yes. Matrix questions appear in the SSC non-verbal and the number reasoning.

How much time should I take?

About 40 seconds.

What is a Latin square?

A matrix in which each figure occurs once in each row and each column.

How can I improve at matrix questions?

By practising and learning the common rules.

Can the rule change between rows?

Usually not; the same rule applies to all rows.

What does overlapping mean?

Placing the first two figures on each other to get the third.