After listening to Car Talk this weekend, I was inspired to create the following question: We have an inexhaustible supply of *travelers* each of whom can carry up to 1 day's worth of rations (we measure the distance in days of travel time). One of them, designated the pilgrim, wants to set off across the dessert from an oasis, aided by a cohort of n other travelers -- the helpers. Each of his helpers can travel a certain distance, transfer some of his rations to the remaining travelers (pilgrim plus remaining helpers) and turn back to the oasis (and thus needs to keep enough rations to allow him to get there). After the last helper leaves, the pilgrim keeps going. When he runs out of rations a magical genie appears and creates a new oasis for him. Let L[n] denote the longest distance (in days) that the pilgrim can travel using n helpers. It's clear that L[n] <= 2 since the last helper to leave can't be more than 1 day's distance away from the oasis. It seems intuitively clear that as n ---> infinity that L[n] ----> 2. Indeed one can work out a recursion for L[n] and solve for it explicitly. However, is there a simple, non-computational proof of this fact which doesn't involve solving for L[n]?