Math CentralQuandaries & Queries


Question from Donessa, a student:

write the number that is 2000 more than the difference between the
largest and the smallest
number that can be formed using the digits 1,2,3,4,5,8,9

Hello Donessa,

I assume that we cannot repeat digits (if we could there would be no “largest” number) and that we must use all of the listed digits.  Our answer will vary depending on our assumptions.
If we must use all of the digits and not repeat then our largest number is obtained by writing the digits in descending order.
i.e. the number 9854321
Can you see why this is true?  What about the smallest number?  How do we know it is the smallest?
What is the difference between these two numbers?
What number is 2000 more than the difference?


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