The puzzle is as follows:
Vincent is a scientist and is about to begin a journey in Antarctica, as he must reach his laboratory at the next station. However, the only buggy available at the base station is undergoing engine maintenance and cannot be used. For this reason he must go on foot. According to his map the trip will take 8 days. However, the weight of supplies that he can carry in his backpack will only last 5 days. For this reason, he needs to recruit one or more assistants since they can carry a weight for 5 days of supplies. The supplies can be shared between Vincent or his assistant. For example, if only the helper's supplies are consumed between him and Vincent on a day of the expedition. The assistants' supplies will last for only 3 days. Since it is required that the assistants must return safely to the base camp without running out of supplies, what is the least number of assistants which Vincent needs to recruit?
The alternatives in my book are as follows:
- 5 assistants
- 6 assistants
- 3 assistants
- 2 assistants
This problem is from my Reason and Logic book of puzzles and seems to be an adaptation from a reprinted version of Martin Gardner's 70s book of Puzzle Carnival.
This problem has left me go in circles too many times. Can someone help me?
I attempted to sketch the situation.
Assuming Vincent is on point A (base camp) and his laboratory on point B:
For this scenario:
Vincent would advance to a point in between $AB$ which I would call $C$:
Since he cannot move forward because his supplies don't last enough to complete the expedition, the problem mentions that he must recruit some helpers to carry more supplies. So in the preceding sketch point C is Vincent plus a helper.
Since the helper can also carry supplies for 5 days, he can advance the same distance attained by Vincent but he cannot return without taking Vincent's supplies with him, therefore, if he only recruits one, it will be insufficient to fulfill his needs. So he must recruit more than one.
This is the part where it becomes troublesome:
Vincent would advance with his helpers to a short distance, they would share some supplies, sufficiently enough for him to keep advancing and to ensure that at least one helper return safely. But we will get to a point where the distance covered by Vincent and his helpers is wide enough to constrain the further advancing without compromising the helpers safely return. So this means that a set of helpers will stand by along the path to act as a relay network allowing a safely return.
At least this is what I concluded. But I don't know how to put this into a graphic or a sketch. Can someone help me with an answer analyzing this strategy? I mean using a visual aid to illustrate how this voyage is taken? I'm sorry if this is too much for a puzzle which may seem easy but for me, I find it some confusing because I'm getting tangled with paths. Can an answer include the requested feature as mentioned lines above? Overall, is my analysis or logic good?