*Originally posted by jimslyp69*

**If the first is 1000 then the second 999, 998 etc, then you could in theory go sequentially all the way down to 500 before the criteria was matched. That means you would need to pick 501 balls out. ðŸ˜€**

that's not everything, because you can pick after those 500 balls, you can pick number 1-166, match the criteria...

EDIT

if you pick out all balls from 501-1000, you picked 500 balls.

If you pick every number under the 166 (501/3-1) which isn't a devision by 2 or 3... you got all balls I think.

That's around 550-600 balls...

EDIT:

you can pick then 84-166, 14-27, 3-4, that's 500+83+14+2+1 (last ball, which guarantees it) balls, so that's.... 600 balls exactly!

I like such puzzles, you need some math, and some logic thinking, I like it both ðŸ˜€ðŸ˜›