Final answer:
The rule for creating a number system using all possible 4 place value patterns is to use all possible combinations of the digits from 0 to 9 in each place value position.
Step-by-step explanation:
To create a rule for a number system using all possible 4 place value patterns, we need to consider the digits in each place value position. Let's take an example. In the first place value, we can have any digit from 0 to 9. In the second place value, we can also have any digit from 0 to 9.
Similarly, in the third and fourth place values, we can have digits from 0 to 9. This gives us a total of 10 choices for each place value. Therefore, the rule for this number system would be to use all possible combinations of the digits from 0 to 9 in each place value position. Using this rule, we can create 16 patterns by considering all the possible combinations of digits in the four place value positions.