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### Finding a Sequence of Numbers

```Date: 08/13/2002 at 18:28:28
From: Kirsti
Subject: Algebra

There are six digits in a sequence: two 4's, two 5's, and two 6's.
There is one digit between the two fours; there are two digits between
the two fives; and there are three digits between the two sixes.
Write this sequence of numbers.

My problem is I can't figure the answer to this question; that's why
I came here.

I have tried many things to figure it out and I have looked in books
from the library, I have asked my teacher, I have asked my parent's,

Thank You!
```

```
Date: 08/13/2002 at 21:22:09
From: Doctor Ian
Subject: Re: Algebra

Hi Kirsti,

It's important to attack a problem like this systematically, so that
you don't end up trying the same answers over and over again, like
someone wandering lost in the woods.

The sequence will look like this:

_ _ _ _ _ _

There is one digit between the two 4's, so that means the following
are the only possibilities:

4 _ 4 _ _ _

_ 4 _ 4 _ _

_ _ 4 _ 4 _

_ _ _ 4 _ 4

Now, there are two digits between the two 5's. Let's look at each of
our possibilities, and see which ones can be extended to take this
second condition into account. In each case, there is only one
possibility:

4 _ 4 _ _ _   =>  4 5 4 _ 5 _

_ 4 _ 4 _ _   =>  _ 4 5 4 _ 5

_ _ 4 _ 4 _   =>  5 _ 4 5 4 _

_ _ _ 4 _ 4   =>  _ 5 _ 4 5 4

In which of these sequences can you insert a pair of 6's that will be
separated by three digits?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
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