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Hmm, okay, that makes sense. Okay, I was never great at math, so dumb question. Doesn't the 8x8x8x8 rule mean that you will have no two combinations with the same digits no matter how they are ordered? Meaning 0001 is not distinguished from 0010 or 0100 or 1000?
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No, they are different codes. 0010 is different and distinguishable from 0100.
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I guess I was thinking if you went through starting with 0001, then 0002, 0003, 0004..... all the way through 7777 (don't know why I was thinking 7799 earlier), then wouldn't you have 7777 codes minus the reserved ones?
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Remember, no 8's or 9's:
1st code = 0000
2nd code = 0001
3rd code = 0002
4th code = 0003
5th code = 0004
6th code = 0005
7th code = 0006
8th code = 0007
*************
9th code = 0010
10th code = 0011
11th code = 0012
12th code = 0013
13th code = 0014
14th code = 0015
15th code = 0016
16th code = 0017
*************
17th code = 0020
18th code = 0021
19th code = 0022
20th code = 0023
21st code = 0024
22nd code = 0025
23rd code = 0026
24th code = 0027
*************
25th code = 0030
>
>
>
>
4095th code = 7776
4096th code = 7777
Starting to see the pattern? There are only 8 digits used in each column, not the normal 10. If all ten were used there would be 10 x 10 x 10 x 10 = 10,000 possible codes (remember that 0000 counts as one code as well, therefore 10,000 possible instead of 9,999). The same math applies to base eight numbering system as base 10. Thus 8 x 8 x 8 x 8 = 4,096 possible codes.
Here is another example, only using base 2 (binary, like computers, use only 1's and 0's) instead of base 8 (0-7) or base 10 (0-9). Might be a little clearer to see.
1st code = 0000
2nd code = 0001
3rd code = 0010
4th code = 0011
5th code = 0100
6th code = 0101
7th code = 0110
8th code = 0111
9th code = 1000
10th code = 1001
11th code = 1010
12th code = 1011
13th code = 1100
14th code = 1101
15th code = 1110
16th code = 1111
Only 2 possible digits in each column, therefore 2 x 2 x 2 x 2 = 16 possible codes.
Cool, eh?
