I have created T-shirt designs with a mathematical theme, and I sell them on http://www.zazzle.com/mathart. Lately, I created a magic trick using mathematics and some other tricks for 'guessing' a number that a volunteer has secretly chosen. Then I adapted this magic trick, in a simpler form, for a T-shirt design. For those who buy the "WHAT IS NUMBER" T-shirt (or receive one as a gift), here is an explanation of how to use the T-shirt as a magic prop. To buy the T-shirt, go to http://www.zazzle.com/what_number_magic_shirt-235678841307212061?rf=238851269352169293 (you can customize the shirt.)
You
ask a volunteer to choose a number in the range 1 to 144, but to keep
it secret. You ask him to find his number on the front of the shirt,
and to tell you the letter in the same box as his number. For
example, he tells you "U". You ask him to also find his
number on the back of the shirt, and to tell you the corresponding
letter. While he is finding his number on the back, you translate
the "U" to 4, using the mnemonic "foUr", and
multiply the 4 by 12, getting 48. He reports "S" for the
back, and you translate the "S" to 6, using the mnemonic
"Six", and add the 6 to the 48, getting 54. You tell him
his number is 54, without (of course) telling him how you derived
that number, and he is amazed.
Optionally, you may ask the volunteer to write down his number on a card and to show the card to others nearby. This allows others to participate by verifying that your 'guess' is correct. It is obvious that you cannot see the back of the T-shirt, but you should not look down at the front of the T-shirt, either. Look straight at the volunteer, or the audience, or look up, or close your eyes, or be blindfolded. The audience may think you have the entire shirt memorized, but that is not necessary.
What
is the complete method, and how does it work? The method is based on
the following matrix and the cipher that follows.
Matrix of numbers 1 to 144 with rows and columns labelled
B
|
I
|
W
|
H
|
U
|
R
|
S
|
E
|
A
|
N
|
T
|
M
|
|
B
|
144
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
I
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
W
|
24
|
25
|
26
|
27
|
28
|
29
|
30
|
31
|
32
|
33
|
34
|
35
|
H
|
36
|
37
|
38
|
39
|
40
|
41
|
42
|
43
|
44
|
45
|
46
|
47
|
U
|
48
|
49
|
50
|
51
|
52
|
53
|
54
|
55
|
56
|
57
|
58
|
59
|
R
|
60
|
61
|
62
|
63
|
64
|
65
|
66
|
67
|
68
|
69
|
70
|
71
|
S
|
72
|
73
|
74
|
75
|
76
|
77
|
78
|
79
|
80
|
81
|
82
|
83
|
E
|
84
|
85
|
86
|
87
|
88
|
89
|
90
|
91
|
92
|
93
|
94
|
95
|
A
|
96
|
97
|
98
|
99
|
100
|
101
|
102
|
103
|
104
|
105
|
106
|
107
|
N
|
108
|
109
|
110
|
111
|
112
|
113
|
114
|
115
|
116
|
117
|
118
|
119
|
T
|
120
|
121
|
122
|
123
|
124
|
125
|
126
|
127
|
128
|
129
|
130
|
131
|
M
|
132
|
133
|
134
|
135
|
136
|
137
|
138
|
139
|
140
|
141
|
142
|
143
|
The
front of the T-shirt indicates which row, and the back of the T-shirt
indicates which column. The letters are translated to numbers
according to the following cipher. The mnemonics are an aid to
memorizing the cipher.
Cipher and mnemonics:
W
|
2
|
tWo, first
spelled number with W
|
H
|
3
|
tHree, first
spelled number with H
|
A
|
8
|
sounds like Ate
|
T
|
10
|
Ten, fourth
spelled number with T
|
I
|
1
|
I looks like 1
|
S
|
6
|
Six, first
spelled number with S
|
N
|
9
|
NiNe, first
spelled number with two N's
|
U
|
4
|
foUr, first
spelled number with U
|
M
|
11
|
eleven –
Melvin (similar sound)
|
B
|
0
|
B00, surprise,
O looks like 0
|
E
|
7
|
sEvEn, first
spelled number with two separate E's
|
R
|
5
|
fiveR, slang
for 5-dollar bill
|
After
translating the front and back letters to numbers Fr and Bk,
calculate this in your head:
Result = 12 * Fr + Bk
You can calculate the 12 * Fr part while the back number is being found.
The Reverse Trick
You can do the magic trick in reverse. That is, given 54, for example, you can determine where it is found without looking. You divide 54 by 12, getting the quotient 4 and remainder 6. Using the cipher, you convert the quotient 4 to U, the position on the front of the shirt, and you convert the remainder 6 to S, the position on the back of the shirt.Another Trick
For any letter, there is a number that appears under that letter on both the front and the back of the T-shirt. So you can ask a volunteer to choose a letter, and then you choose a number that appears under that letter on both the front and the back. To do this, it will help to be familiar with the multiples of 13. (Most people are not, and as a result, think that 91 is a prime number.)Given a letter, use the cipher to convert the letter to a number, then multiply the number by 13. For example, suppose the letter is E. According to the cipher, the corresponding number is 7. 7 times 13 is 91, so you declare that 91 is found in box E on both the front and the back of the T-shirt.
The equivalence of 0 and 144 applies to all tricks.
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