Question 923948
<pre>
1989 is a multiple of 3.  If you pick all the multiples of 3

3,6,9,12,...,1989 

any two of them are a multiple of 3 apart and if two integers are
a multiple of 3 apart, they can neither be 4 apart nor 7 apart. 

How many of them are there?

To find out, divide them all by 3 and you have the counting
numbers from 1 through 663

1,2,3,4,...,663

so there are 663 of them.

You can also choose

1,4,7,10,...,1987 or

2,5,8,11,...,1988

There are also 663 of each of them as well.

Answer: 663

Edwin</pre>