How many kittens at least to take You have $7$ boxes in front of you and $140$ kittens are sitting side-by-side inside the
boxes, $20$ in each box. You want to take some kittens as your pets. However the
kittens are very cowardly. Each time you chose a kitten from a box, the kittens that
are in that box to the left of it go to the box in the left, the kittens that are in that box
to the right go to the box in the right. If they don’t find a box in that direction, they
simply run away. After taking a few kittens, you see that all other kittens have run
away. At least how many kittens have you taken?
 A: I would take the outmost left kitty in each box starting from the box on the left and going to the last box on the right, thus all kitten are running right and I would have 7 of them.
You can also take all 140 kittens by alternating left and right so as to concentrate all kittens in the center box. Then each time you pick a kitty, take the outmost right or left in the box they ran into in order to contentrate them again in the center box, and so on until kitten exhaustion.
I still need to think, if it's possible to pick any number between 7 and 140 and all boxes consequently empty. Sounds like a Nim puzzle.
A: To add on zwim's answer (can't comment for reputation)
A kitten only changes it's box, if you choose one from it's box. So you have at least grab into every box to scare all of them away, hence at least 7 kittens. 
The argument about any number of kittens to be taken, can be taken by extending the "all kitten to take" approach by zwim. 
If you want to take $140-X$ kittens, just scare every animal in a single box (i.e. the rightmost) and take $X+1$-th kitten from the right to scare exactly $X$ kitten away. 
Then proceed, as if you want all kittens. 
Edit: Just seen Ojas' comment, that basically uses the same argument, shame on me!
