In a certain cave 2 bats could see out of the right eye, 3 could see out of the left eye, exactly 4 could not see out of the left eye and exactly 5 could not see out of the right eye. What is the smallest number of bats in the cave?

The minimum of bats you can have is 7.

Explanation:

Since the question does not specify if these are different bats or not, we can assume that at least 2 bats can see with both eyes = can see out of their left eye and out of their right eye. We will also assume that there is 1 bat who can see out of his left eye but not his right eye.

Then you'll have the following

2 bats = only see out of their right eye

3 bats = only see out of their left eye

1 bat = Right blinded

We have 3 bats so far.

We can also assume that 4 bats are fully blind.

That leaves us with:

2 bats = good right eye

3 bats = good left eye

5 bats = right blinded

4 bats = left blinded

Trying to rearrange the bats differently will always give out a larger number than 7.