**Can You See The Pattern**

**Page: 99**

**1.**

**Solution :-**

**Solution :-**

**2. What should come next?**

**(a)**

**Solution:-**

**(b)**

**Solution:-**

**(c)**

**Solution:-**

**(d)**

**Solution:-**

**3. See this pattern**

**(a)**

**Solution:-**

**4. Using the same rule take it forward till you get back to what you started with.**

**(a)**

**Solution:-**

**(b)**

**Solution:-**

**Solution:-**

**6. Mark that picture which is breaking the rule. Also correct it.**

**(a)**

**Solution:-**

The below marked picture is breaking the rule.

**(b)**

**Solution:-**

The below marked picture is breaking the rule.

**(c)**

**Solution:-**

The below marked picture is breaking the rule.

**(d)**

**Solution:-**

The below marked picture is breaking the rule.

**7. Magic Squares**

**Do you remember magic triangles? Come now, let’s make some magic squares.**

**(i) Fill this square using all the numbers from 46 to 54.**

**Rule: The total of each line is 150.**

**Solution:-**

From the question it is give that, total of each line is equal to 150.

So, let us take third row,

From the rule, + 52 + 47 = 150

+ 99 = 150

= 150 – 99

Therefore, number in the first box in third row = 51

Now, let us take first column,

From the rule, + 46 + 51 = 150

+ 97 = 150

= 150 – 97

Therefore, number in the first box in first column = 53

Let us take first row,

From the rule, 53 + + 49 = 150

+ 102 = 150

= 150 – 102

Therefore, number in the second box in first row = 48

Let us take second column,

From the rule, 48 + + 52 = 150

+ 100 = 150

= 150 – 100

Therefore, number in the second box in second column = 50

Let us take third column,

From the rule, 49 + + 47 = 150

+ 96 = 150

= 150 – 96

Therefore, number in the second box in third column = 54

**(ii) Fill this square using all the numbers from 21 to 29.**

**Rule: The total of each side is 75.**

**Solution:-**

From the question it is give that, total of each line is equal to 75.

**8. Magic Hexagons**

**Look at the patterns of numbers in hexagons. Each side has 2 circles and 1 box.**

**Look at the number 65 in the box. Which are the circles next to it? Can you see how the rule works?**

**Solution:-**

The circles next to 65 are 5 and 13.

The rule of this method is we get the number in each box by multiplying the numbers in the circles next to it.

**(i) Use the same rule to fill the hexagons below.**

**(a)**

**Solution:-**

11 × 9 = 99

11 × 6 = 66

6 × 17 = 102

17 × 7 = 119

9 × 12 = 108

12 × 7 = 84

**(b)**

**Solution:-**

4 × 16 = 64

16 × 8 = 128

8 × 8 = 64

13 × 8 = 104

13 × 6 = 78

**9. Numbers and Numbers**

**(i) Are they equal?**

**Solution:-**

Yes, the mentioned equation are equal.

Because, let us consider left hand side (LHS) of first equation = 24 + 19 + 37

LHS = 80

Now, Right hand side (RHS) = 37 + 24 + 19

RHS = 80

By comparing LHS and RHS,

LHS = RHS

Then consider second equation, LHS = 215 + 120 + 600

LHS = 935

Now, RHS = 600 + 215 + 120

= 935

By comparing LHS and RHS,

LHS = RHS

**(ii)** **Fill in the blank spaces in the same way.**

**(a)**

**Solution:-**

**(b)**

**Solution:-**

**(c)**

**Solution:-**

**(iii)** **Now,look at this-**

**Check if it is true or not.**

**Solution:-**

First consider the left hand side (LHS) = 48 × 13

LHS = 624

Now consider right hand side (RHS) = 13 × 48

RHS = 624

By comparing LHS and RHS,

LHS = RHS

**(iv) Now you try and change these numbers into special numbers**

**(a) 28**

**Solution:-**

Take another number 28

Now turn it back to front 82

Then add them together 110

Is this a special number? No! Why not?

OK, carry on with the number 110

Again turn it back to front 011

Then add the two together 121

Ah! 121 is a special number.

**(b) 132**

**Solution:-**

Take another number 132

Now turn it back to front 231

Then add them together 363

Ah! 363 is a special number.

**(c) 273**

**Solution:-**

Take another number 273

Now turn it back to front 372

Then add them together 645

Is this a special number? No! Why not?

OK, carry on with the number 645

Again turn it back to front 546

Then add the two together 1191

Is this a special number? No! Why not?

OK, carry on with the number 1191

Again turn it back to front 1911

Then add the two together 3102

Is this a special number? No! Why not?

OK, carry on with the number 3102

Again turn it back to front 2013

Then add the two together 5115

Ah! 5115 is a special number.

**(v) Now let’s use words in a special way.**

**Did you notice that it reads the same from both sides — right to left and left to right?**

**Solution:-**

EYE, LEVEL, ROTATOR, NOON, REFER, TOP SPOT etc.

**10. Some more Number Patterns**

**(i) Take any number. Now multiply it by 2, 3, 4 …………… at every step. Also add 3 to it at each step. Look at the difference in the answer. Is it the same at every step?**

**Solution:-**

Let us check difference in the answer, 39 – 27 = 12, 51 – 39 = 12, 63 – 51 = 12,

75 – 63 = 12, 87 – 75 = 12, 99 – 87 = 12, 111 – 99 = 12.

Therefore, the difference in the answer are same at every step.

**(ii) Look at the numbers below. Look for the pattern. Can you take it forward?**

**Solution:-**

**11. Smart Adding**

**Solution:-**

**(ii)** **Did you notice some pattern in the answers?**

**Solution:-**

Yes, I found that the difference in the answer are same i.e. 100 at every step.

**12. Fun with Odd Numbers**

**Take the first two odd numbers. Now add them, see what you get. Now, at every step, add the next odd number.** **How far can you go on?**

**Solution:-**

We can’t predict, because there are infinite numbers.

**13. Secret Numbers**

**Banno and Binod were playing a guessing game by writing clues about a secret number. Each tried to guess the other’s secret number from the clues. Can you guess their secret numbers?**

**(i) It is larger than half of 100**

**It is more than 6 tens and less than 7 tens**

**The tens digit is one more than the ones digit**

**Together the digits have a sum of 11**

**Solution:-**

It is larger than half of 100, i.e. number > 100

It is more than 6 tens and less than 7 tens = so, number lies between 70 and 60

The tens digit is one more than the ones digit = 6 – 1 = 5

Together the digits have a sum of 11 = 6 + 5 = 11

Therefore the number is 65

**(ii)** **It is smaller than half of 100**

**It is more than 4 tens and less than 5 tens**

**The tens digit is two more than the ones digit**

**Together the digits have a sum of 6**

**Solution:-**

It is smaller than half of 100 = number > 100

It is more than 4 tens and less than 5 tens = number lies between 40 and 50

The tens digit is two more than the ones digit = 4 – 2 = 2

Together the digits have a sum of 6 = 4 + 2 = 6

Therefore the number is 42

**14. Number Surprises**

**a) Ask your friend rite — W down your age. Add 5 to it. Multiply the sum by 2. Subtract 10 from it. Next divide it by 2. What do you get? Is your friend surprised?**

**Solution:-**

Let us assume the age be 11,

Then, adding 5 to it we get = 16

Multiply by 2 we get = 32

Subtract from 10 we get = 22

Divided by 2 we get = 11

Yes, my friend was really surprised.

**Solution:-**

**Solution:-**

**Solution:-**

1 = 1 × 1

121 = 11 × 11

12321 = 111 × 111

1234321 = 1111 × 1111

123454321 = 11111 × 11111

12345654321 = 111111 × 111111

1234567654321 = 1111111 × 1111111

1234567654321 = 1111111 × 1111111

1234567654321 = 1111111 × 1111111