Why does it work?


 

To make this trick work you need to place the numbers from 1 to 63 in the lists in a particular arrangement. Notice that each of the numbers in the upper left corner of a list is a power of two.

32 = 25, 16 = 24, 8 = 23, 4 = 22, 2 = 21 and 1 = 20.

Start to create the lists by putting the powers of 2 in the upper left corners.

 
32            
    
    
    
    
    
    
    
16            
    
    
    
    
    
    
    
8            
    
    
    
    
    
    
    
4            
    
    
    
    
    
    
    
2            
    
    
    
    
    
    
    
1            
    
    
    
    
    
    
    
 

Each integer from 0 to 63 can be written in the form

a x 25 + b x 24 + c x 23 + d x 22 + e x 21 + f x 20 where a, b, c, d, e and f are either 0 or 1. This is often written abcdef2 and called base two notation.

For each number between 1 and 63 first write it in base two notation. For example for 41.

41 = 1 x 32 + 0 x 16 + 0 x 8 + 1 x 4 + 0 x 2 + 1 x 1
     = 1 x 25 + 0 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20
     = 1010012

Place the number on each card that corresponds to a 1 in the base 2 representation. Thus, reading from left to right, 41 is placed on the first, third and sixth cards.

 


 
32333435
36373839
40414243
44454647
48495051
52535455
56575859
60616263
16171819
20212223
24252627
28293031
48495051
52535455
56575859
60616263
891011
12131415
24252627
28293031
40414243
44454647
56575859
60616263
4567
12131415
20212223
28293031
36373839
44454647
52535455
60616263
2367
10111415
18192223
26273031
34353839
42434647
50515455
58596263
1357
9111315
17192123
25272931
33353739
41434547
49515355
57596163
 
 
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