BdMO Online Forum

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?

We need to take minimum amount of kittens.
Firstly, we will take the rightest kitten of the first box. So, the rest $7$ kittens, on the left, will simply run away.
In the $2^{nd}$ box, let the leftest kitten has been taken. So, $7$ kittens at right will go to the $3^{rd}$ box. In the $3^{rd}$ box, there will be $(6+7)=13$ kittens in total.
Next time, let the leftest has been taken from the $4^{th}$ box. So, in the $5^{th}$ box, there will be $(12+7)=19$ kittens in that box.
In this way, $6$ times we will take the leftest kitten and at last, all will simply run away.
So, we will take minimum $7$ kittens in total