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
Arthur, Bob, and Carla each choose a three-digit number. They each multiply the digits of their own numbers.  Arthur gets 64, Bob gets 35, and Carla gets 81. Then, they add corresponding digits of their numbers together.  The total of the hundreds place is 24, that of the tens place is 12, and that of the ones place is 6. What is the difference between the largest and smallest of the three original numbers?

*Proposed by Jacob Weiner*
user
182
rule
Arthur, Bob, and Carla each choose a three-digit number. They each multiply the digits of their own numbers.  Arthur gets 64, Bob gets 35, and Carla gets 81. Then, they add corresponding digits of their numbers together.  The total of the hundreds place is 24, that of the tens place is 12, and that of the ones place is 6. What is the difference between the largest and smallest of the three original numbers?

*Proposed by Jacob Weiner*
train