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Generating all possible permutations and finding the maximum and minimum numbers that satisfy the conditions takes the following Python program around 5.4s:

We can unroll the loop and do early rejection of numbers that fail the condition in the early digits. That’s a longer program, but runs in 163ms.

However, if we set up the initial list correctly we can use the order that permutations are generated by Python to find only the first solution. Which gives us the maximum and minimum numbers in 31ms.

Solution:The largest such number is 9876351240. The smallest is 1234897560.