Q: What is the largest 5 digit number not using the same number twice?

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You get the largest number if you sort the digits, from largest to smallest.

543210

99997

For this type of "the largest number which..." questions, you need to advance from left to right, using the largest possible digit in each case. For the first two digits, that would be 9, for the third digit (the right-most digit), the largest digit which will make this possible is an 8.

874321 is the largest number made from all these digits.

88,888

99,997

998,000

Pressumably, you want to use each digit once. Starting from the left, use the largest digit you can every time. For example, the left-most digit should be "6".

943

9,876,543,210

If you mean only using nines then 99.