Registered: Jan 2004
Posts: 350

Here is a simple mechanism for reading out whatever is in a "black box".

Whenever you multiply modulo three sum the contents of the "black box" by logical 1 (rule number: 3812798742493), you get the contents of the "black box" as a result without changing the "black box" contents.

The example below verifies this for a random sampling of 32 rule numbers over the range of all possible three color, three variable rule numbers.

Union[FromDigits[
     Mod[IntegerDigits[3812798742493, 3, 27] IntegerDigits[#, 3, 27], 
      3], 3] == # & /@ Table[RandomInteger[{0, 7625597484986}], {32}]]

{True}

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L. J. Thaden

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