The context is that of a pandemic that is spreading wildly and requiring global vaccination of the population.
You are working in a distribution center for the vaccines.
One day you have been requested to prepare and deliver 40 boxes of vaccines to 3 vaccination centers. You have a minivan and will do a roundtrip visiting each center once.
Unfortunately you haven't been told how many boxes each vaccination center needs. You will learn the need of each center only when you arrive there. It could even be that a center didn't order any vaccine for that day. You just know the total is 40 boxes.
The problem is that the boxes need to be delivered in refrigerated sealed containers. You can't reopen any container when delivering the boxes. You must deliver the containers still sealed.
You don't have to deliver exactly one container per center. You could just put each box in its own container. But it is a lot of work to refrigerate and seal a container. And you are lazy. So you want to figure out a better way to arrange boxes in containers in such a way that you are sure, regardless of the needs of each vaccination center, that you can deliver to each one the exact number of boxes they need.
Of course, you want to minimize the number of containers you need to prepare.
So, how many containers do you prepare and how many boxes do you put in each container?
Disclaimer: The events portayed in this puzzle are fictitious. Any resemblence to real events or situations is purely coincidential.
PS: clarification: The unit is the box, which is indivisible. The number of doses per box is irrelevant. All boxes are equal. The vaccination centers ordered an integer number of boxes. You cannot return boxes. You must pack exactly 40 boxes.