Talk:A. W. Faber Model 366

Python program to check property

Here's a small Python program to check the mathematical properties of the table given in the illustration:

table = """                                                                     
       0  1 69  2 24 70  9  3 38                                                
   25 13 71 66 10 93  4 30 39 96                                                
   26 78 14 86 72 48 67  7 11 91                                                
   94 84  5 82 31 33 40 56 97 35                                                
   27 45 79 42 15 62 87 58 73 18                                                
   49 99 68 23  8 37 12 65 92 29                                                
   95 77 85 47  6 90 83 81 32 55                                                
   34 44 41 61 57 17 98 22 36 64                                                
   28 76 46 89 80 54 43 60 16 21                                                
   63 75 88 53 59 20 74 52 19 51                                                
   50                                                                           
"""

s = dict(zip(range(1, 101), map(int, table.split())))

for i in range(1, 101):
    for j in range(1, 101):
        x = (s[i] + s[j])%100
        y = s[(i*j)%101]
        if (x != y):
            raise Exception("mismatch")

print "all matched"

And here's the mapping inverted, from s[i] to i, where s[i] is the table generated above, for i=0 to i=99:

[1, 2, 4, 8, 16, 32, 64, 27, 54, 7, 14, 28, 56, 11, 22, 44, 88, 75, 49, 98, 95, 89, 77, 53, 5, 10, 20, 40, 80, 59, 17, 34, 68, 35, 70, 39, 78, 55, 9, 18, 36, 72, 43, 86, 71, 41, 82, 63, 25, 50, 100, 99, 97, 93, 85, 69, 37, 74, 47, 94, 87, 73, 45, 90, 79, 57, 13, 26, 52, 3, 6, 12, 24, 48, 96, 91, 81, 61, 21, 42, 84, 67, 33, 66, 31, 62, 23, 46, 92, 83, 65, 29, 58, 15, 30, 60, 19, 38, 76, 51]

which also happens to be the sequence of numbers you can see on the Schumacher-system scale in the image seen here. Code for this:

d = dict(zip(map(int, table.split()), range(1, 101)))

print [d[i] for i in range(0, 100)]

-- The Anome (talk) 22:12, 9 April 2021 (UTC)