You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
In the game "set," all possible four-digit numbers consisting of the digits 1, 2, and 3 (each digit used exactly once) participate. A triplet of numbers is said to form a set if, for each digit position, either all three numbers have the same digit, or all three numbers have different digits.

The difficulty of a set is defined as the number of digit positions where all three digits are different.

For example:
- The numbers 1232, 2213, and 3221 form a set of difficulty 3 (in the first position all three digits are different, in the second position only the digit 2 is present, in the third position all three digits are different, and in the fourth position all three digits are different).
- The numbers 1231, 1232, and 1233 form a set of difficulty 1 (in the first three positions the digits are the same, and only in the fourth position all three digits are different).
- The numbers 1123, 2231, and 3311 do not form a set at all (in the last position there are two ones and one three).

Which difficulty level sets are most numerous in the game and why?
user
3
rule
In the game "set," all possible four-digit numbers consisting of the digits 1, 2, and 3 (each digit used exactly once) participate. A triplet of numbers is said to form a set if, for each digit position, either all three numbers have the same digit, or all three numbers have different digits.

The difficulty of a set is defined as the number of digit positions where all three digits are different.

For example:
- The numbers 1232, 2213, and 3221 form a set of difficulty 3 (in the first position all three digits are different, in the second position only the digit 2 is present, in the third position all three digits are different, and in the fourth position all three digits are different).
- The numbers 1231, 1232, and 1233 form a set of difficulty 1 (in the first three positions the digits are the same, and only in the fourth position all three digits are different).
- The numbers 1123, 2231, and 3311 do not form a set at all (in the last position there are two ones and one three).

Which difficulty level sets are most numerous in the game and why?
train