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The greatest 5 digit number is 98765. The greatest 5 digit number that doesn't contain any of those digits is 43210. The difference between them is 55555.

The two five digit numbers using all ten digits once and only once between them that sum to the largest value are 97531 and 86420. They sum to 183,951 and have a difference of 11111. These two numbers are not unique ... you can switch any pair of digits between the two numbers as long as you keep them in the same position without changing the sum, though this will change the difference.

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Q: What is the difference between the greatest 5 digit number and the greatest 5 digit number with all different digit?
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