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Number puzzles
5
You have done a lot of calculations and now you are going to use
what you have learnt to solve some puzzles.
➜➜Missing numbers
In the next exercise, there are some calculations just like the
ones you have been doing in previous chapters – but some of the
numbers are missing.
Exercise 5.1
Copy these calculations and fill in the missing numbers.
1
4
8
+
1
2
5
6
1
5
2
1
3
8
8
0
3
–
4
7
3
7
3
5
4
7
+
1
0
3
6
5
1
8
8
7
3
5
9
8
2
0
×
4
– 6
4
1
2
1
5
8
7
5
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7
8
5
×
2
2
4
7
8
5
4
1 7 4
8
4
0
6
5
5
−
−
➜➜Missing operations
In Chapter 2 you learnt about the order of operations, which is
summarised as BIDMAS.
In the next exercise, some of the operations are missing. You have
to work them out by looking at the numbers.
Examples:
Fill in the correct operation, +, −, × or ÷, to make each calculation correct.
(i) 9
6 = 15 (ii) 4
6=8
3
(iii) (8
6)
12 = 36
(i) 9 + 6 = 15
15 is larger than 9 or 6 so consider + or ×
(ii) 4 × 6 = 8 × 3
You have two calculations that have the same answer.
(iii) (8 × 6) – 12 = 36 Make sure that you use the brackets correctly.
Exercise 5.2
1 15
7=8
6 9
5
3=7
2 36
9=4
7 6
9
5=3
8
6=4
3 8 = 26
18
8 3
4 24 = 8
3
9 12
57
3 = 10
6
10 8
3=9
4
4 = 36
3
5
Number puzzles
Fill in the correct operation, +, −, × or ÷, to make each calculation correct.
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3 = 24
3
1516
8
128
6 = 12
6
168
6=8
(12
Using symbols
119
2=4
13(5
4)
2=2
1712
(8
2) = 9
1412
(8
2) = 2
18(6
3)
4=8
3)
(16
(24
2)
6)
➜➜Using symbols
In the questions above you had some numbers, but sometimes you
may only have an answer. You are used to questions such as:
If the cost of three buns is 96p, what is the cost of one bun?
but the question could look like this:
● + ● + ● = 96
You still solve this in the same way, by dividing by 3, so the answer is:
● = 32
Example:
Find the value of ●, ■ and ▲ in these three statements.
● + ● = 24
● + ■ = 20
● + ■ + ▲ = 26
● = 24 ÷ 2
So ● = 12
Then 12 + ■ = 20
■ = 20 – 12
So ■ = 8
And 12 + 8 + ▲ = 26
So ▲ = 6
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Exercise 5.3
Find the value of the symbols in each of these questions.
1 ● + ● = 18
5 ❖ + ❖ + ❖ = 20 − ]
● + ■ = 12
] + ★ = (❖ + ❖) × 3
2 ◆ + ◆ + ◆ = 18
◆+■=9
3 ● + ● + ● = 24
● + ■ = 12
● + ■ + ◆ = 21
4 ●+●+●=9
● + ■ + ■ = 15
● + ■ = 20 − ◆
] + ★ = 24
6 ★ + ] + ] = 13
★−]=4
❖ + ❖ + ❖ + ❖ + ❖ = 2 × (★➜+ ])
7 ●+●=■
●×●=■
● + ■ + ◆ = 11
8 ●×●=●
●+■=■+◆
● + ■ + ◆ = 10
For this set of questions there are no symbols but just words.
Use exactly the same methods as before, to solve these.
9 The sum of two numbers is 13 and their difference is 3
What are the numbers?
10 A silver medal weighs twice as much as a bronze medal. A bronze medal
and two silver medals weigh the same as a gold medal. How many bronze
medals weigh the same as a gold medal?
12 A box of paints and a drawing book costs £3.50. A paintbrush and a drawing
book costs £1.50. Three paintbrushes cost 72p. How much does a box of
paints cost?
5
Number puzzles
11 If two cakes cost 90p and one cake and one bun costs 75p, what is the
cost of three buns?
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Function machines
13I can buy three apples and two bananas for 85p, or two apples and one
banana for 50p. What is the cost of:
(a)one apple and one banana
(b)two apples?
14Two widgets and one fidget cost £11 but one widget and two fidgets
cost £13
What is the cost of one widget and one fidget?
15 Look at this menu.
1 egg and tomato
80p
1 egg and chips£1.10
1 egg, chips and tomato£1.40
What would be the cost of two eggs, chips and tomato?
16I can buy one pen and two pencils for £1.50, or two pencils and one
eraser for 70p or one pen, one pencil and one eraser for £1.45
I decide to buy one pen and one pencil. How much will that cost me?
➜➜Function machines
Imagine that you put a number into a machine and another number
comes out. Look at this machine.
5➞
1➞
➞ 7
+ 2
3➞
➞ 3
➞ 5
You can see that each of the numbers that comes out is 2 more
than the number that went in, as the machine is a ‘plus 2’ machine.
This is a ‘multiply by 3’ machine. You can see what comes out – but
not what went in.
➞ 9
a➞
b➞
c➞
× 3
➞ 12
➞ 15
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As 3 × a = 9, then a = 3
As 3 × b = 12, then b = 4
As 3 × c = 15, then c = 5
Exercise 5.4
Calculate the value of the missing numbers that come in or out of these
function machines.
1
5➞
1➞
2
3
➞ a
➞a
➞ b
1 ➞
c➞
➞ 12
c ➞
➞8
5➞
➞ a
9 ➞
➞a
8➞
+4
5 ➞
−3
c ➞
4
➞ b
18 ➞
➞ 14
c ➞
×2
÷3
➞b
➞b
➞4
In the next questions there are two machines. Work out the missing numbers
in them.
5
5➞
1➞
➞ 8 ➞
+3
e➞
×3
➞ c➞
➞c
➞8
➞ a➞
f ➞
➞b
−4
➞d
➞8
➞ e➞
In these next sets of machines you may also need to work out what function
is in the machine.
7 12 ➞
8 ➞
➞ 14
➞a➞
−5
c ➞
➞b➞
➞6 ➞
A
➞ 6
➞ d
5
Number puzzles
×2
➞ d ➞
6 0 ➞
5 ➞
➞ b ➞
➞a
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5 ➞
➞ 16 ➞
E
➞ 8 ➞
➞ a
F
➞ 32 ➞
b ➞
Using symbols again
8 13 ➞
➞ 2
➞ 8
➜➜Using symbols again
In the previous exercise the symbols stood for numbers. Sometimes
you have puzzles where the symbols stand for operations.
Examples:
On the planet Antaeon the symbol ‡ stands for ‘add them together and
subtract 1’
So 3 ‡ 2 = 3 + 2 – 1
= 4
(i) What is the value of: (a) 4 ‡ 3 (b) 5 ‡ (5 ‡ 2)
(c) (3 ‡ 7) ‡ (5 ‡ 2)?
(ii)If a ‡ b = 5 what are the possible values of a and b?
(i) (a) 4 ‡ 3 = 4 + 3 − 1
=6
(b) 5 ‡ (5 ‡ 2) = 5 ‡ (5 + 2 − 1)
=5‡6
=5+6−1
= 10
(c) (3 ‡ 7) ‡ (5 ‡ 2) = (3 + 7 − 1) ‡ (5 + 2 − 1)
=9‡6
=9+6−1
= 14
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(ii) If a ‡ b = 5
a + b−1 = 5
a + b= 6
Possible values of a and b are 1 and 5, 2 and 4, 3 and 3, 4 and 2, 5 and 1
Exercise 5.5
1 The symbol ♦ means ‘add them together and multiply the answer
by 3’, so 5 ♦ 4 is 3 × (5 + 4) = 27
(a) Find the value of:
(i) 3 ♦ 1 (ii) 2➜♦ 2 (iii) 6➜♦ (5➜♦ 4) (iv) (4➜♦ 2) ♦ (5 ♦ 1)
(b) If a ♦ b = 9 and a and b are not equal what are the possible
values of a and b?
2 The symbol means ‘half of the sum’ so 5 3 means
(5 + 3) ÷ 2 = 4
(a) Find the value of:
(i) 4 2 (ii) 7 2 (iii) 5 (4 6) (iv) (10 4) (12 6)
(b) If a b = 1 1 and a and b are not equal, what are the possible
2
values of a and b?
3 The symbol ♣ means ‘the product less the sum’ so 5 ♣ 4 means
(5 × 4) − (5 + 4) = 11
(a) Find the value of:
(i) 3 ♣ 4 (ii) 5 ♣ 3 (iii) 5 ♣➜(4 ♣ 2) (iv) 3 ♣➜(3 ♣➜(3 ♣ 3))
4 The symbol ♦ means ‘double the sum then subtract 3’
(a) Find the value of:
(i) 4 ♦ 1 (ii) 7 ♦ 3 (iii) (2 ♦ 7) ♦ 5) (iv) (5 ♦ 1) ♦ (3 ♦ 3)
(b) If a ♦ b = 5 and a and b are not equal, what are the possible
values of a and b?
5
Number puzzles
(b) If a ♣ b = 0 what are the possible values of a and b?
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Sequences
5(a)Look at these calculations and work out the meaning of the
symbol ♦
5 ♦ 2 = 20
6 ♦ 3 = 36
4 ♦ 7 = 56
(b)Find the value of 4 ♦ 3
6(a)Look at these calculations and work out the meaning of the
symbol
5
2 = 20
6
(b)Find the value of 4
3 = 26
4
7 = 32
3
7(a)Look at these calculations and work out the meaning of the
symbol
4 2 = 6
6 3 = 15
(b)Find the value of 5
8 5 = 37
3
➜➜Sequences
A sequence is a list of numbers or objects that are in a special order.
Each number is a term. If the terms are numbers, you can calculate
the ‘difference’, that is how much larger or smaller one term is than
the one before it.
Example:
Find the difference between the consecutive terms and then work out the
next two terms in this sequence.
3, 5, 7, 9, 11, …
When finding missing numbers in a sequence, you can write the difference
between the terms with little arcs, like this.
+2
3,
+2
5,
+2
7,
+2
9,
+2
11,
+2
13,
15
The difference is + 2 and the next two terms are 13 and 15
Some sequences are very simple, as in the example above, but in
the next exercise there are some special sequences that you should
look out for.
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Exercise 5.6
1 Simple sequences
Look at this sequence.
4, 7, 10, 13, 16, …
(a) Write down the pattern of differences in this simple sequence.
(b) How would you describe this sequence?
(c) What are the next three numbers in the sequence?
2 Square numbers
(a) Count the dots in these patterns and then work out the next three
numbers in the sequence.
(b) Write down the pattern of differences in the sequence of square
numbers.
(c) How would you describe this sequence?
3 Triangular numbers
(a) Count the dots in these patterns and then work out the next three
numbers in the sequence.
(b) Write down the pattern of differences in the sequence of triangular
numbers.
(c) How would you describe this sequence?
4 Fibonacci numbers
Number puzzles
The Fibonacci sequence is:
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
This is a very special sequence. To find out why, you need to look at the
differences.
5
(a) Write down the pattern of differences in the Fibonacci sequence.
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Sequences
(b)How would you describe this sequence?
(c)How would you work out the next number in the sequence?
(d)What is the next number?
5 Two-step sequences
Sometimes the pattern of differences in a sequence is not
simple. You will need to use + and − to describe it.
Look at this sequence.
5, 8, 7, 10, 9, 12, 11, …
(a)Write down the pattern of differences in this sequence.
(b)How can you describe this sequence?
(c)What are the next three numbers in the sequence?
6 Embedded sequences
If none of the above seems to work, you may have two
sequences embedded in one.
Look at this sequence.
5, 4, 10, 7, 15, 10, 20, 13, …
Look at it again, like this.
5, 4, 10, 7, 15, 10, 20, 13, …
(a)What is the pattern of differences in the red numbers?
(b)What is the pattern of differences in the black numbers?
(c)What are the next three numbers in the sequence?
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➜➜Finding missing terms
In the next exercise you are going to find the missing terms in the
sequences. Remember to work out the differences first and then see
what type of sequence you have.
Examples:
Find the missing terms in each sequence.
(i) 4, 7, 10, 13, …, …
(ii) 0, 3, 8, 15, …, …
(iii) 2, 5, 7, 12, 19, …, …
(iv) 1, 3, 2, 6, 4, 9, …, …
(i) +3
+3
4,
7,
+3
+3
10,
13,
+3
16,
19
This is a simple sequence with a difference of + 3
(ii) +3
0,
+5
3,
+9
+7
8,
15,
+11
24,
35
he differences form a sequence of odd numbers so this is based on
T
the sequence of square numbers.
These are ‘square numbers – 1’
(iii) +3
2,
+2
5,
+7
+5
7,
12,
+12
19,
+19
31,
50
Aside from the first the differences are the same as the terms.
This is a Fibonacci-type sequence.
(iv) +2
1,
–1
3,
–2
+4
2,
6,
+5
4,
9,
…,
…
There is no obvious pattern to the differences.
5 Number puzzles
Try alternate terms.
×2
1,
3,
×2
2,
+3
6,
×2
4,
+3
9,
8,
12
+3
This is a + 3 sequence embedded in a × 2 sequence.
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Finding missing terms
Exercise 5.7
Find the missing terms in each sequence.
1 6, 11, 16, 21, 26, …, …
8 0, 3, 3, 6, 9, 15, …, …
2 4, 8, 12, 16, 20, …, …
9 7, 1, 9, 3, 11, 5, …, …
3 4, 9, 16, 25, 36, …, …
10 6, 1, 9, 3, 12, 9, …, …
4 2, 5, 10, 17, 26, …, …
11 9 1, 8, 6 1, 5, 3 1, …, …
5 1, 3, 6, 10, 15, …, …
12 65, 59, 68, 62, 71, …, …
6 0, 2, 5, 9, 14, …, …
13 4, 2, 8, 4, 16, …, …
7 1, 1, 2, 3, 5, 8, …, …
14 1, 4, 5, 9, 14, 23, …, …
2
2
2
More missing terms
In the next exercise the missing terms are not just at the end. As
before, calculate the differences and spot the pattern. As you will
be adding and subtracting, multiplying and dividing, take care to
check your final answer.
Examples:
Find the missing terms in these sequences.
(i) 1, …, 7, 10, …, 16
(ii) …, …, 5, 8, 13, 21
(i)
+3
1,
+3
4,
+3
+3
7,
+3
10, 13, 16
This is a simple sequence with a difference of + 3
(ii)
+1
2,
+2
3,
+5
+3
5,
8,
+8
13, 21
The differences are the same as the terms, so this is a
Fibonacci-type sequence.
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Exercise 5.8
Find the missing terms in each sequence.
1 1, 4, …, …, 25, 36, 49
8 81, 64, …, 36, …, 16
2 …, …, 6, 10, 15, 21, 28
9 …, 16, 3, 26, …, 36, 5
3 121, 100, …, 64, …, 36
10 …, 19, 14 1, 10, …, 1
4 2, …, 12, 17, …, 27
11 …, 2 1, 5, 8 1, …, 18 1
5 1, 3, …, 7, …, 18, 29
12 2, 6, …, 54, …, 486
6
13 1, 11, …, 6, …, 1
2
7 …, 11, 3, 21, 5, …, 7
2
2
2
2
13 2, …, 5, 8, 12, …, 23
14 10, 7, 17, …, 41, 65, …
➜➜Number puzzles
For this last exercise, you need to use the information that you
know about numbers to solve the puzzles.
Exercise 5.9
1 I have two numbers with a sum of 11 and a product of 24
What are the numbers?
2 I have two numbers with a sum of 17 and a product of 60
What are the numbers?
3 I have two numbers with a difference of 4 and a product of 60
What are the numbers?
5 (a) A number that is less than 20 has remainder 2 when divided
by 3, and remainder 3 when divided by 4
What is the number?
(b) Write a calculation that includes 3 and 4 to explain your answer.
5
Number puzzles
4 I have two numbers with a difference of 13 and a product of 90
What are the numbers?
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Number puzzles
6 (a) A number that is less than 20 has remainder 2 when divided
by 3, and remainder 4 when divided by 5
What is the number?
(b) Write a calculation that includes 3 and 5 to explain your answer.
7 (a) A number that is less than 100 has remainder 3 when divided
by 4, remainder 4 when divided by 5 and remainder 5 when
divided by 6
What is the number?
(b) Explain your answer.
8 When I divide a two-digit number by 4 the remainder is 2 and when
I divide it by 7 the remainder is 5
What is the smallest number I could have started with?
9 When I divide a two-digit number by 6 the remainder is 4 and when
I divide it by 8 the remainder is 6
What is the largest number I could have started with?
10 I remember the four digits on my padlock like this.
The last digit is four times the first, and the third digit is three times
the second but one less than the fourth.
What is my number?
Activity – Consecutive number investigation
Consecutive numbers follow directly after one another, such as 5, 6, 7
5 + 6 + 7 = 18
Are there any other ways of adding consecutive numbers to make 18?
Repeat this exercise to find consecutive number sums for numbers 10 to 30
Write down any rules or patterns you notice.
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5
Number puzzles
This chapter covers the following elements of the National Curriculum for Year 6:
Number: addition, subtraction, multiplication and division
● Programme of study (statutory requirements)
Pupils should be taught to:
• use their knowledge of the order of operations to carry out calculations involving
the four operations.
● Notes and guidance (non-statutory)
• Pupils explore the order of operations using brackets; for example, 2 + 1 × 3 = 5 and
(2 + 1) × 3 = 9
Algebra
● Programme of study (statutory requirements)
Pupils should be taught to:
• generate and describe linear number sequences
• find pairs of numbers that satisfy an equation with two unknowns
• enumerate all possibilities of combinations of two variables.
● Notes and guidance (non-statutory)
• Pupils should be introduced to the use of symbols and letters to represent variables and
unknowns in mathematical situations that they already understand, such as missing
numbers and number puzzles (e.g. what two numbers can add up to).
This chapter also covers the following elements not mentioned in the National Curriculum:
●
●
●
●
Function machines
Symbols for operations
Visual approach to simultaneous equations
Sequences including square, triangular and Fibonacci number sequences
ICT can be used in the following ways:
● Pupils could use a spreadsheet to explore their number patterns.
Notes
n It is not intended that this whole chapter should be done in one go. Each exercise stands alone, as a piece
of mathematical reasoning. The exercises can be done at any time, in any order (except for the three
sequences exercises which should be done consecutively).
n Questions found in these exercises are similar to those set on examination papers for this age group.
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Exercise 5.1
2
4
5
8
5
6
1
1
0
1
3
4
6
5
7
3
4
7
3
1
1
+
2
−
2
4
3
5
×
6
−
8
0
0
3
6
4
2
8
1
5
7
5
5
5
4
7
3
8
5
2
2
0
0
2
5
8
5
2
4
4
0
8
3
4
7
×
3
4
1
8
1
2
8
1
4
8
5
+
2
1
2
3
9
8
4
4
8
7
7
3
6
8
5
9
0
8
2
7
6
8
6
8
−
−
5
Number puzzles
Exercise 5.2
 1 1
5
−
7
=
8
 2 3
6
÷
9
=
4
 3 8
=
2
6
−
1
 4 2
4
=
8
×
3
 5 7
+
6
−
3
=
1
 6 9
−
5
+
3
=
7
 7 6
+
9
÷
5
=
3
8
0
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5
×
8
÷
6
=
4
 9 1
2
×
3
=
9
×
4
10 8
+
4
=
3
6
÷
3
11 9
×
3
=
2
4
+
3
12 8
−
6
=
1
2
÷
6
13 (5
−
4)
×
2
=
2
14 1
2
÷
(8
−
2)
=
2
15 1
6
÷
8
+
2
=
4
16 8
−
6
=
8
÷
(1
2
÷
3)
17 1
2
×
(8
−
2)
=
9
×
(1
6
÷
18 (6
−
3)
×
4
=
8
+
(2
4
÷
6)
Exercise 5.3
1
●=9
n=3
2
u=6
n=3
3
●=8
n=4
u=9
4
5
6
●=3
n=6
u = 11
❖=4
=8
★ = 16
★=7
=3
❖=4
Number puzzles
 8 3
2)
 7 ● = 2
n=4
u=5
 8 ● = 1
u=1
n=8
 9 8 and 5
105
1190p
12£2.24
13 (a)35p (b) 30p
14£8
15£1.90
16£1.25
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Exercise 5.4
1 a = 9, b = 5, c = 8
5 a = 16, b = 4, c = 8, d = 4, e = 1
2 a = 2, b = 5, c = 17
6 a = 0, b = −4, c = 15, d = 11, e = 12, f = 4
3 a = 10, b = 2, c = 4
7 a = 7, A = times 2, b = 3, c = 11, d = 12
4 a = 3, b = 6, c = 12
8E = plus 3, F = divide by 4, a = 4, b = 29
Exercise 5.5
1(a)(i) 12
(ii) 12
(iii) 99
(iv) 108
(iii) 5
(iv) 8
(ii) 7
(iii) 3
(iv) 3
(ii) 17
(iii) 37
(iv) 33
(b)
1 and 2 or 2 and 1
2(a)(i) 3
1
(ii) 4 2 (b)
1 and 2 or 2 and 1
3(a)(i) 5
(b)
2 and 2
4(a)(i) 7
(b)
1 and 3 or 3 and 1
5(a)Double the product
(b) 24
6(a)Multiply the sum by three and subtract 1
(b) 20
7(a)The product minus the difference
(b) 13
Exercise 5.6
1(a)+3, +3, +3, +3
(b)
A simple +3 sequence
(c)
19, 22, 25
2(a)16, 25, 36
(b)
+3, +5, +7, +9, +11
(c)
Differences are a sequence of odd numbers.
3(a)10, 15, 21
(c)
Differences are a sequence of consecutive (or counting) numbers.
4(a)0, +1, +1, +2, +3, +5, +8, +13, +21
(b)
Differences are the same as the sequence of terms.
(c)
Add two terms together.
(d)
34
5
Number puzzles
(b)
+2, +3, +4, +5, +6
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6 (a) +3, +3, +3
5 (a) +3, −1, +3, −1, +3, −1
(c) 14, 13, 16
(c) 25, 16, 30
Exercise 5.7
1
1
1
1
1 6, 11, 16, 21, 26, 31, 36
6 0, 2, 5, 9, 14, 20, 27
2 4, 8, 12, 16, 20, 24, 28
7 1, 1, 2, 3, 5, 8, 13, 21
11 9 2 , 8, 6 2 , 5, 3 2 , 2, 2
12 65, 59, 68, 62, 71, 65, 74
3 4, 9, 16, 25, 36, 49, 64
8 0, 3, 3, 6, 9, 15, 24, 39
13 4, 2, 8, 4, 16, 6, 32
4 2, 5, 10, 17, 26, 37, 50
9 7, 1, 9, 3, 11, 5, 13, 7
14 1, 4, 5, 9, 14, 23, 37, 60
5 1, 3, 6, 10, 15, 21, 28
10 6, 1, 9, 3, 12, 9, 15, 27
Exercise 5.8
1 1, 4, 9, 16, 25, 36, 49
1
1
1
1
1
1
2 1, 3, 6, 10, 15, 21, 28
6 13 2 , 11, 8 2 , 6, 3 2 , 1
7 1, 11, 3, 21, 5, 31, 7
11 1, 2 2 , 5, 8 2 , 13, 18 2
12 2, 6, 18, 54, 162, 486
3 121, 100, 81, 64, 49, 36
8 81, 64, 49, 36, 25, 16
13 2, 3, 5, 8, 12, 17, 23,
4 2, 7, 12, 17, 22, 27
9 2, 16, 3, 26, 4, 36, 5
14 10, 7, 17, 24, 41, 65, 106
5 1, 3, 4, 7, 11, 18, 29
10
Number puzzles
(b) +5, +5, +5
5
(b) Two-step +3 − 1 sequence
1
1
1
23 2 , 19, 14 2 , 10, 5 2 , 1
Exercise 5.9
1 8 and 3
3 6 and 10
2 5 and 12
4 5 and 18
5 (a) 11
(b) 11 = 3 × 3 + 2 = 4 × 2 + 3 (other answers may be correct)
6 (a) 14
(b) 14 = 3 × 4 + 2 = 5 × 2 + 4 (other answers may be correct)
7 (a) 59
(b) 59 = 4 × 14 + 3 = 5 × 11 + 4 = 6 × 9 + 5 (other answers may be correct)
8 26
9 94
10 1134
Activity – Consecutive number investigation
You cannot make 16 (or 2, 4, 8)
All odd numbers can be written as the sum of a pair of consecutive numbers.
Sums of consecutive numbers starting with 1 are triangle numbers.
Multiples of 3 can always be written as sum of 3 consecutive numbers.
Numbers that are 2 more than a multiple of 4 can be written as sum of 4 consecutive numbers.
Multiples of 5 (not 5 or 10) can always be written as the sum of 5 consecutive numbers.
3 × odd number greater than 5 can always be written as sum of 6 consecutive numbers.
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