<p>how many positive integers less than 1000 are NOT divisible by 3.</p>
<p>Take 1000 and divide it by 3. You get 333.33 and truncate that to just 333. This is the number of positive integers that ARE divisible by 3. So subtract 1000 from 333 and you get 667 positive integers that are NOT divisible by 3.</p>
<p>The answer is 666. I guess you count the thing u truncated as 1. but great solution. I was trying to use permutations like a fool haha.</p>
<p>The way I did it was:</p>
<p>0<x<1000</p>
<p>999 numbers/3 = 333 divisible by 3. 999-333 = 666.</p>
<p>edit-nevermind.</p>
<p>Oops sorry. I see what I messed up. I included 1000 in my calculation. So it should have been just 999 - 333 like CalDud did.</p>