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Inverse operations – spy codes
a
b
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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
The code shown above gives each letter as its position in the alphabet. So maths would be given as 13 1 20 8 19.
You could make the code harder to crack by applying the same calculation to each number, to create a new code. This
example shows the code being changed with the expression 2x + 3:
2x + 3
letter
a
b
c
d
e
position
1
2
3
4
5
code
5
7
9
11 13
If someone wanted to crack the code, they would have to know the calculation you used and apply the inverse operations to
decode each number back into its alphabetical position:
2x + 3
© www.teachitmaths.co.uk 2012
inverse: ½(x – 3)
code
19 13 27 27 33
position
8
5
letter
h
e
20121
12 12 15
l
l
o
Page 1 of 3
Inverse operations – spy codes
Work out the inverse for each expression, then use it to convert the numbers back into alphabetical positions to decipher each
message:
1. 3x – 2
58
67
inverse =
43
25
55
58
22
13
43
40
21
41
34
73
13
64
13
40
27
5
39
6
45
46
52
25
37
17
13
41
43
48
39
15
13
40
61
43
49
33
6
57
6
37
4
13
9
30
12
52
inverse =
2. 2x + 3
13
21
17
19
43
11
21
17
21
43
53
41
33
31
13
37
45
5
39
13
12
48
42
18
60
-
33
6
9
57
31
43
19
13
45
29
7
13
21
57
48
42
39
inverse =
3. 3(x + 1)
6
39
24
18
9
72
48
57
15
:
57
:
6
6
39
-
Extension: Create your own message and code for a classmate to decipher.
You will need to:
1. Write a short message. Underneath each letter, write down its alphabetical position.
2. Choose an expression to create your code. This can be anything you like, but using division can get messy! Use your expression to change
each number into your new code. Keep your workings in a safe place so you can use them to give the correct answer.
3. On a new piece of paper, write out your coded message and the expression you used, then swap with a classmate. Decode each other’s
messages by working out the inverse operations to change each number back into an alphabetical position.
© www.teachitmaths.co.uk 2012
20121
Page 2 of 3
Inverse operations – spy codes
Answers
1. 3x – 2
inverse = 1/3(x + 2)
58
67
43
25
55
58
22
13
43
40
34
73
13
64
13
40
46
52
25
37
13
40
61
37
4
13
52
t
w
o
i
s
t
h
e
o
n
l
y
e
v
e
n
p
r
i
m
e
n
u
m
b
e
r
inverse = ½(x – 3)
2. 2x + 3
13
21
17
19
43
53
33
31
13
21
41
43
19
13
27
5
39
17
13
41
43
43
49
33
e
i
g
h
t
y
o
n
e
i
s
t
h
e
l
a
r
g
e
s
t
t
w
o
11
21
17
21
43
41
37
45
5
39
13
31
45
29
7
13
39
d
i
g
i
t
s
q
u
a
r
e
n
u
m
b
e
r
inverse =
3. 3(x + 1)
6
39
24
18
9
57
6
12
48
42
18
60
21
57
48
42
6
45
48
39
15
6
57
6
9
30
12
a
l
g
e
b
r
a
c
o
m
e
s
f
r
o
m
a
n
o
l
d
a
r
a
b
i
c
72
48
57
15
:
6
39
-
33
6
9
57
w
o
r
d
:
a
l
-
j
a
b
r
© www.teachitmaths.co.uk 2012
20121
Page 3 of 3