Number Grids & Magic Squares
Finding missing values in grids, tables, and magic squares
Explanation
Magic Squares
In a magic square, every row, column, and diagonal adds to the same number — the magic sum.
Example 3×3 magic square (magic sum = 15):
| 2 | 7 | 6 |
| 9 | 5 | 1 |
| 4 | 3 | 8 |
Finding the Magic Sum
For a magic square using numbers 1 to n²:
- Sum of all numbers = n²(n² + 1) ÷ 2
- Magic sum = Total sum ÷ n
- 3×3: Total = 45 → Magic sum = 45 ÷ 3 = 15
In exam questions, just add any complete row or column to find the magic sum.
Grids with Arithmetic Rules
Some grids use operations across rows or columns.
Example: Each row multiplies to 24. Find the missing value (?):
| 2 | 4 | 3 |
| 6 | ? | 2 |
Strategy & Key Tips
- Find the magic sum (or rule) using a complete row or column.
- For each incomplete row/column, subtract known values from the magic sum.
- Verify that all rows, columns, and diagonals match.
Key Tips
- At least one complete row or column is always given — use it to establish the rule
- Diagonals must also equal the magic sum — use them to double-check your answers
- For non-magic-square grids, identify the operation (add, multiply) by testing a complete row
- Work from rows/columns with only one unknown value — solve these first
Sample Practice Questions
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In a table, each row follows: (first × second) + third. Row: 3, 4, 2 → 14. What does 5, 2, 3 give?
Show answer
Answer: 13
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A 3×3 magic square uses numbers 1 to 9. What is the magic sum?
Show answer
Answer: 15
-
A magic square row sums to 21. Two numbers in the row are 8 and 6. What is the third number?
Show answer
Answer: 7
-
What is 7 × 6?
Show answer
Answer: 42
Practice Questions
Test your knowledge of Number Grids & Magic Squares with a timed quiz. Answers are revealed at the end.
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What does Number Grids & Magic Squares cover in the Selective Entry Numerical Reasoning exam?
Finding missing values in grids, tables, and magic squares.
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