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### Integer Sequence

```
Date: 08/30/97 at 00:50:08
From: windows
Subject: Integer sequence

Show that if 19 distinct integers are chosen from the sequence
1,4,7,10,13,16,19..........,97,100, there must be two of them
whose sum is 104.
```

```
Date: 09/03/97 at 10:47:03
From: Doctor Rob
Subject: Re: Integer sequence

List all the pairs that add up to 104:

4,100
7,97
10,94
...
46,58
49,55

There are 16 pairs. The numbers 1 and 52 are not included.  If you
choose 19 numbers, at least 17 must be chosen from the 16 pairs, ...

I hope this helps.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Sequences, Series

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