Yes, in that problem, you can have the first helper go for 1 day, distribute 1 day's worth to the other two left, and turn back. After another 1 1/2 days, the remaining helper gives 1 1/2 days rations to the pilgrim and turns back, who then can travel for 6 1/2 days in total (more than enough). This is the maximum distance with two helpers. If there is only one helper, the best he can do is to go for 4/3 of a day, and give 4/3 to the pilgrim and turn back. But then the pilgrim can only go 5 1/3 days in all, which is easy to see is a maximum. On Thu, Jul 5, 2012 at 12:49 PM, Michael Beeler <mikebeeler@verizon.net>wrote:
I think the answer to the original Car Talk puzzle does not scale, in that 2 pilgrims can reach the destination by using less than 2 times the helpers.
--- spoiler alert ---
Car Talk asks for delivery of 1 pilgrim a distance of 6 days travel away, and each person can carry a max of 4 days rations. I think 2 helpers are required, but one helper returns with 1 day worth of unused rations. (Alternatively, the party can depart with only 11 person-days of rations.)
If the party is allowed to hide rations along the way, 3 helpers can deliver 2 pilgrims, a delivery rate of 2/5 that is > 1/3. 5 depart fully loaded. After 1 day, there are 15 person-days of rations left. The next morning, 2 pilgrims and 1 helper continue forward, each fully loaded. 2 helpers return to base, each with 1 day of rations. And 1 day of rations is hidden at the overnight location.
It seems like there should be some parameters that would lead to helpers turning back, and/or stashing rations, at fractional days distance, but I don't see an example case.
-- Mike
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