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### Finding Number Patterns

```
Date: 05/29/99 at 23:01:16
From: Sam Thorsheim
Subject: Pattern problem

I am trying to find the pattern in the numbers
3, 8, 13, 18, 23, 28, 30, 31, 32...
```

```
Date: 05/30/99 at 14:20:11
From: Doctor Sorelle
Subject: Re: Pattern problem

Dear Sam,

What have you thought of so far? That's always useful to know, so next
time you submit a question, please include that information.

For problems like this my first step is always to see if the
differences between the numbers are the same. For example:

3, 6, 9, 12, 15, 18...

in the pattern above you'd notice that the number goes up by 3 each
time.

Sometimes it can be a little more complicated:

1, 2, 4, 7, 11, 16, 22...

In this problem the differences between the numbers are 1, 2, 3, 4,
5...

So there are lots of different patterns that change by the number
added to them each time.

If none of these options (or options like these) works (as I suspect
they won't in your problem) it's time to look at the problem more

The next thing that I would do is see what sorts of numbers are used
in the problem, whether they have any mathematical-looking relation.
Here's an example...

1, 10, 100, 1000

I bet you can tell what the pattern is there.

Now you come to the point where you're ready to give up and write Dr.
Math (always a good option ;-) ), but wait! There's another type of
pattern it might be. It's the type of pattern that ONLY has to do
with the numbers involved, for example...

1, 12, 123, 1234, 12345...

These numbers as a whole have nothing to do with each other, but the
digits that make them up are in a pattern. Or...

1, 11, 111, 1111, 11111...
or...
1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41...

Can you see what the pattern is in this last one? Think about it for a
minute... Did you figure it out?

In the last pattern the numbers included all had the number 1 in them,
or, to put it another way, they were all numbers with the digit 1 in
them. I think it's this last type of pattern that's going to help you
solve your pattern. I know you can do it - good luck!

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

```
Date: 05/31/99 at 10:19:52
From: mark thorsheim
Subject: Re: Pattern problem

I see the pattern of multiples of 5 after the first number 3, but get
stuck at the 31 and 32.
```

```
Date: 05/31/99 at 19:21:00
From: Doctor Sorelle
Subject: Re: Pattern word problems

Hi-

I'm sorry, it looks like as if my answer got cut off above. That must
have made it a little confusing. Let's see if I can straighten things
out.

What I was going to say is that in the pattern that I gave you as an
example, the numbers had nothing to do with each other other than that
they all had the digit 1 in them. The other patterns had nothing to do
with this type.

Here's another example pattern...

2, 4, 12, 14, 20, 21, 22, 23, 24...

In this pattern (very similar to the one you're trying to 'decode')
there are two digits that are key. Every number has one or both of
these digits (2 and 4). To make this pattern, I chose every number
that had one or both of those digits in them. It didn't matter how far
they were spaced apart or anything like that. The only thing that
mattered were the digits in the numbers - whether they had a 2 or a 4
in them.

Think you have it? Write back if you have more questions!

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

```
Date: 06/01/99 at 16:06:12
From: mark thorsheim
Subject: Re: Pattern problem

Okay - that helps a lot. Thank you.
```
Associated Topics:
High School Sequences, Series

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