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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?

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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!

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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.

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    Yes, I think any number between 7 and 140 is possible. Just do the following : If you're picking a kitten from the leftmost box, pick the leftmost kitten. Similarly, pick the rightmost kitten from the rightmost box. If you're picking a kitten from any of the other boxes, pick any kitten. No kitten will ever run away. – 2017-01-06
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    I agree, but I want the boxes to be empty after having picked N kitten. If I take 6 of them always from leftmost non empty box, then 134 of them are concentrated in the rightmost box. If I pick the rightmost (7) kitty, 133 go to the left box. I take the leftmost (8) and 132 of them are again in the rightmost box. I take the leftmost (9) again and all kitten ran away. So I achieved 9 kitten ! This is not a correct strategy for 8 kitten. – 2017-01-06
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    Oh ok! Misunderstood you. Anyways, I think even that is possible. After you've picked 6 kittens using your strategy, all the rest are in the rightmost box. Now, if you want $N$ kittens in the end, just pick the $(N-6)^{th}$ kitten from the left. $140-N$ kittens will run away. Now pick all the kittens as I described above. – 2017-01-06
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    Yes, that is working ! – 2017-01-06
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    You didn't prove that at least 7 kittens are taken. – 2017-01-06
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    To empty all the boxes you need at least to take 1 kitten per box because untouched boxes won't empty otherwise. So 7 is the minimal number. And if you did it as described picking always the leftmost kitten, then you effectively empty all boxes. What more do you want ? – 2017-01-06