Marist College Ashgrove
Benjamin Lister
Math’s A
Year 11
Task 1
Question 1
a) Construct a graph of the frequency of Scrabble letters in a set
Total number of Scrabble tiles in a set is 100.
There are 26 letter tiles and 2 blank tiles in the game of Scrabble.
The table below shows how many tiles there are per letter
LETTER TILE
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
BLANK
NUMBER OF TILES IN SET
9
2
2
4
12
2
3
2
9
1
1
4
2
6
8
2
1
6
4
6
4
2
2
1
2
1
2
b) Construct a graph of the tile scores
NUMBER OF POINTS ON TILES
0 points
1 point
2 points
3 points
4 points
5 points
8 points
10 points
LETTERS WITH THOSE POINTS
BLANK/WILD
E, A, I, O, N, R, T, L, S, U
D, G
B, C, M, P,
F, H, V, W, Y
K
J, X
Q, Z
aa) Comment on the similarities and differences between parts (a) and (b).
(MPS)
The similarities between a and b can be seen in both graphs as how the most uncommonly used letters have a higher point score. As can be seen for the most common letters they have a lower score because they are more frequently used.
Question 2
a) Calculate the mean frequency for each letter, rounded to the nearest whole number?
LETTER
TOTAL
MEAN
ROUNDED MEAN
A
381
8.466666667
8
B
87
1.933333333
2
C
109
2.422222222
2
D
169
3.755555556
4
E
536
11.91111111
12
F
74
1.644444444
2
G
106
2.355555556
2
H
270
6
6
I
316
7.022222222
7
J
11
0.244444444
0.2
K
58
1.288888889
1
L
191
4.244444444
4
M
117
2.6
3
N
291
6.466666667
6
O
347
7.711111111
8
P
79
1.755555556
2
Q
5
0.111111111
0.1
R
247
5.488888889
5
S
283
6.288888889
6
T
421
9.355555556
9
U
145
3.222222222
3
V
45
1
1
W
108
2.4
2
X
6
0.133333333
0.1
Y
94
2.088888889
2
Z
5
0.111111111
0.1
b) Which is the most common letter in the combined sample?
The most common letter in the combined sample is E for its total is 536
c) Which are the 4 most common letters?
The four most common letters where E, J, A, P
d) Which letters do not occur at all?
Letters that didn’t occur where J, Q, X, Z
e) Compare your results from APPENDIX A with the scrabble frequencies from Question 1 and comment on any differences you find. (MPS)
Question 3
a) Using your analysis (in Question 1 and 2) you should be able to identify the two most common letters used in the English language. See if you can use that and the additional information given above to decode the following message.
LJUF UFLLQEFL QGF VFXZ LFHGFZ SJZ DR DFISE FSHJOFO DMZ DR DFISE
KIOOFS JSF JA ZKF UJLZ MSMLMQP UFZKJOL MLFO DR ZKF EGFFVL TQL ZJ
LKQBF ZKF KFQO JA ZKF UFLLFSEFG ZQZZJJ ZKF UFLLQEF JS KIL LHQPX QSO
ZKFS LFSO KIU JSHF ZKF KQIG KQO EGJTS DQHV SJZ JSF AJG SFWZ OQR
OFPIBFGR
The above code translates to:
SOME MESSAGES ARE KEPT SECRET NOT BY BEING ENCODED BUT BY BEING
HIDDEN. ONE OF THE MOST UNUSUAL METHODS USED BY THE GREEKS WAS
TO SHAVE THE HEAD OF THE MESSENGER TATTOO THE MESSAGE ON HIS
SCALP AND THEN SEND HIM ONCE THE HAIR HAD GROWN BACK NOT ONE FOR
NEXT DAY DELIVERY.
b) List any assumptions you have made. Explain why you have made these assumptions ● I identified the most common letters in the pattern and also referred to the frequency table.
● Worked on the smaller word pattern ZKF that occurs 6 times.
● Using the most common letters ‘T’ and ‘E ‘was able to assume ‘K’ was an
‘H’.
● Assumed ‘S’ in ‘ZKFS’ was an ‘W’ and inserted into the text.
● Assumed ‘J’ was an ‘O’ as this made sense of the two letter words.
● ‘ZQZZJJ’ with other information because ‘TQTTOO’ meaning ‘Q’ has to be
‘A’
Chart showing letter equivalent
O H E G U Q J S K Z I
D C G R M A O N H T I
A M P X B R D W V K T
F U L P V Y B X K H W
TASK 2
Question 4
Using this method of coding, encode the message below using the ‘KEY’:
Multiply by 5 and then add 2.
Plaintext:
“Pure mathematics is, in its way, the poetry of logical ideas” Albert
Einstein.
Numerical Translation:
15, 20, 17, 4, 12, 0, 19, 7, 4, 12, 0, 19, 8, 2, 18, 8, 18, 8,
13, 8, 19, 18, 22, 0, 24, 19, 7, 4, 15, 14, 4, 19, 17, 24, 14, 5, 11, 14, 6, 8, 2, 0, 11, 8, 3,
4, 0, 18, 0, 11,
