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### Ordering Digits

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Date: 08/15/98 at 18:48:04
From: Jessica Hardage
Subject: Math

I just entered the 7th grade, and our math teacher gave us a question
to figure out:

Using the digits 6 1 4 8 3 9, write the largest counting number that
is smaller than 5,000 and write the smallest counting number that is
greater than 5,000. Each number in the number 6 1 4 8 3 9 may not be
used more than once.
```

```
Date: 08/17/98 at 13:11:43
From: Doctor Peterson
Subject: Re: Math

Hi, Jessica.

I'll give you a few questions that should get you started. First,
which digits could you use for the first digit of the number and
still have less than 5000? Which digits would you have to start with
to keep the number bigger than 5000?

Second, in each case, which of the possible digits would you choose to
make the answer as close to 5000 as possible?

Third, how can you choose and arrange the remaining three digits so
that they are as large or as small as possible?

As another example, if I have to use the digits 2, 5, and 7 to make a
three-digit number, what order should I put them in to make that number
as large as possible? The first digit will have the most value, so I
should put the largest possible digit there: 7__. (You should be able
to see that 2__ and 5__ would always be smaller than this.) The second
digit is more valuable than the third, so you should make the most of
it by using the largest of the digits you have left: 75_, which leaves
one digit for the last place: 752. This is the sort of reasoning you
will have to use.

- Doctor Peterson, The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
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