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On a dartboard scoring a double 18 and a treble 18 results in a score of 90.

Complete the Sum 4

Complete the sum challenges mix numbers and logic. Pupils must spot hidden rules or patterns to fill in the blanks and balance equations successfully.

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Fascinating Fact:

In ancient China magic squares were used where numbers in every row, column and diagonal all added to the same total.

In 11-Plus Verbal Reasoning, complete the sum puzzles encourage learners to practise arithmetic, logical deduction, and problem-solving. They make maths interactive and enjoyable while sharpening thinking skills.

Key Terms

Magic Square: A grid where the sums of numbers in each row, column, and diagonal are the same.
Equation: A statement showing two things are equal, often including numbers and symbols.
Reasoning: Using logic to reach a conclusion or solve a problem.

Frequently Asked Questions (Click to see answers)

What is a magic square in maths?

A magic square is a grid where the numbers are arranged so each row, column, and diagonal add up to the same total.

How do complete the sum puzzles improve reasoning?

They improve reasoning by requiring pupils to find missing numbers using logic, number patterns, and problem-solving skills.

Where were magic squares first used?

Magic squares were first used in ancient China, where they were studied for both mathematical and cultural importance.

Try These Related Quizzes

Example:

26 + 7 = 18 + ?

13
14
15
16

Answer: 15

This is because 26 + 7 = 33. 18 + ? = 33. This makes 15 the only possible answer.

1 .

Find the number that will complete the sum below correctly.

27 - 13 = 42 ÷ ?

This is because 27 - 13 = 14. 42 ÷ 3 is also equal to 14. The first three square numbers are 1, 4 and 9. 14 is the sum of these square numbers

2 .

Find the number that will complete the sum below correctly.

63 ÷ 9 = 32 - ?

This is because 32 - 25 = 7 and 63 ÷ 9 = 7

3 .

Find the number that will complete the sum below correctly.

4 x 16 = ? - 55

117

119

This is because 119 - 55 = 64, which is the same as 4 x 16. That was one to get your brain working a little harder! Did it work, or are you an expert at these questions now?

4 .

Find the number that will complete the sum below correctly.

79 + ? = 9 x 9

This is because 9 x 9 = 81. To get to this product from 79 we have to add 2

5 .

Find the number that will complete the sum below correctly.

56 ÷ 8 = ? - 8

This is because 56 ÷ 8 = 7. This is the same as 15 - 8. A cubed number is a number multiplied by itself and then by itself again (for example, 3 x 3 x 3 = 27, making 27 the cube of 3 and 3 the cube root of 27). Can you work out the cube root of 8? Read below for the answer

6 .

Find the number that will complete the sum below correctly.

39 ÷ 3 = ? - 18

This is because 39 ÷ 3 = 13, which is equal to 31 - 18

7 .

Find the number that will complete the sum below correctly.

? - 45 = 8 x 4

This is because 77 - 45 = 32 and 8 x 4 = 32. Remember the challenge we set you in question 5? Did you work out that the cube root of 8 is 2?

8 .

Find the number that will complete the sum below correctly.

72 - 14 = ? x 2

This is because 29 x 2 = 58. Also, 72 - 14 = 58

9 .

Find the number that will complete the sum below correctly.

? ÷ 13 = 90 ÷ 18

This is because 90 ÷ 18 = 5 and 65 ÷ 13 = 5. Only 65 works. On a dartboard scoring a double 18 and a treble 18 results in a score of 90. What would a treble and a double 19 score? Read below for the answer

10 .

Find the number that will complete the sum below correctly.

27 x 3 = 9 x ?

This is because 27 x 3 = 81 and 9 x 9 also equals 81. The answer to the little quiz in question 9 is 95 (19 x 3 = 57 and 19 x 2 = 38. 57 + 38 = 95). We hope you enjoyed this series of quizzes, and look forward to you trying the next series of Verbal Reasoning quizzes!

Author: Stephen O'Hara