# Form 1 Unit 1: Lesson 5 – Number Puzzle

Lesson
Materials

Objective:

At the end of the lesson, students should be able to solve number puzzles.

Many puzzles using addition and subtraction have developed over the years. One well known puzzle is the magic square.

Magic squares are a kind of puzzle in which numbers are put in small squares and their sum across the squares should match up to their sum along the square and along the diagonals.

Example 1

Complete this magic square Solution

The magic number here is 15 The example above shows that the total along any straight line is equal to 15. The total is called the magic number.

Example 2

Find the value of A and B if Solution

Since each letter represents the same digit throughout the coded puzzle we could try A = 1 therefore 11 1 = 11 which means the answer would also be AA.

If we try A = 2 we get 22 2 = 44

So A = 2 and B = 4.

Example 3

Which number will replace the question mark? Solution

In each row there are ‘A‘, ‘B‘ and ‘C

In the second row ‘A‘ and ‘C‘ are already there

Hence in place of?, there will be ‘B’.

From first row: 4A x 6C = 24B

From third row: 9B x 4C = 36A

From second row: 5A x ? = 45C

? = (45C/5A)

? = 9B

Hence the number 9B will replace the question mark.

Example 4
If ‘AND’ is written as ‘EQF’ and ‘THE’ as ‘XKG’ then how will ‘COM’ be written?

Solution

if AND is written as, Similarly, ‘COM’ be written as; Example 5

Which number will replace the question mark? Solution

From fig. a: 6 + 4 + 8 = 18

18 + 2 = 20

From fig. b: 7 + 9 + 8 = 24

24 + 2 = 26

From fig. c: 6 + 5 + 12 = 23

23 + 2 = 25

Hence the number 25 will replace the question mark.

Example 6

Which number will replace the question mark? Solution

From fig. a: (3)2 + (2)2 = 13

From fig. b: (4)2 + (8)2 = 80

From fig. c:? = (1)2 + (5)2

? = 1 + 25

? = 26

Hence the number 26 will replace the question mark.

Example 7

Which number will replace the question mark? Solution

From fig. a: 92 + 82 + 72 + 62 = 81 + 64 + 49 + 36 = 230

From fig. b: 62 + 72 + 32 + 42 = 36 + 49 + 9 + 16 = 110

From fig. c: 92 + 62 + 52 + 42 = 81 + 36 + 25 + 16 = 158

Hence the number 158 will replace the question mark.

Example 8

Which number will replace the question mark? Solution

(4 + 3)2 = (7)2 = 49

(8 + 5)2 = (13)2 = 169

(11 + 12)2 = (23)2 = 529

(10 + 9)2 = (19)2 = 361

Hence the number 361 will replace the question mark.

Example 9

Which number will replace the question mark? Solution

From fig. a: (8 x 5) – (4 x 3) = 40 – 12 = 28

From fig. b: (12 x 7) – (8 x 9) = 84 – 72 = 12

From fig. c: (5 x 3) – (6 x ?) = 21

15 – 6? = 21

6? = -6

? = -1

Hence the number -1 will replace the question mark.

Example 10 Solution

Adding the three numbers in each square together gives the numerical value of the letter at the centre of each square

Example 11 Solution

Add together values in corresponding positions of the top two crosses, and put the results in the lower left cross. Calculate the difference between values in corresponding positions of the top two crosses, and put the results in the lower right cross. Finally, add together the values in corresponding positions of the lower two crosses to give the values in the central cross.

Strategies For Solving Puzzle Problems

• Read the question at least twice, it is always a good start to make sure you understand the problem.
• Then read the question again.
• Look for patterns – each puzzle is usually different so you have to look for the patterns that apply to each puzzle problem.
• Guess and check.
• Work backwards if possible.
• Solve the puzzle.

Unit 1 Lesson 5: Exercise 1  CHECK ANSWERS  AT LESSON MATERIAL ( AT THE TOP OF THE LESSON ) Explanation: Looking at the line of numbers from top;
9 x 8 = 72
72 x 8 = 576
576 x 8 = 4608

Explanation: Looking across the three circles, the number in the middle is the product of the two numbers in the same segment in the other two circles. i.e;
3 x 2 = 6, 7 x 3 = 21 and 4 x 4 = 16. Explanation: Numbers follows the alternate of prime numbers
3 + 7 + 9 + 12 + 10 = 41
4 + 6 + 10 + 9 = 31
7 + 9 + 7 = 23
5 + 12 = 17
So the next prime number is 13 then 11, etc.

Explanation: Add the two oval and divide the result by two to get the bigger oval, i.e. (47 + 63) ÷ 2 = 55, (85 + 99) ÷ 2 = 92, (73 + 25) ÷ 2 = ?, ? = 49

Explanation: Looking at the line of number from the top two boxes add up to give the next box below it. i.e. 6 + 7 = 13 and 7 + 2 = 9
Next row; 13 + 9 = 22
Fourth row; 17 + 5 = 22
Last row; 13 + 4 = 17
4 + ? = 5
Therefore, 5 – 4 = ?
? = 1.

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