Ranger Cadet Bu Star has just been given the task of moving the five cases of Park Pop soda at the Weiss Pavilion to the Wirth Pavilion, which is 5 miles away. For transport, Bu must use a MoJoPed, a moped which runs on Park Pop. It can carry, at most, its rider and 25 bottles of soda, i.e., one case in its cargo carrier and one bottle in its fuel tank. It gets one mile to the bottle and is currently empty; it will only move under Pop power. How many unopened bottles can Bu deliver to the second pavilion?
Comments to triflers:
The bottles and cases are hi-tech, so there are no concerns about theft or littering. They can stay parked or be discarded anywhere. Yes, the constant rate of fuel use is unreal, and yes, of course, I am asking for the maximum number of bottles!
Hint
There are hints in the comments to triflers and in the title.
Answer
80
To achieve this surprising result, Bu must first take the five cases, one at a time, and park them at a point along the route miles from the Weiss Pavilion. This takes 9 trips of miles (5 advancing trips interspersed with 4 return trips) for a total of 20.5 miles travelled (9 * = 20.5) and 20.5 bottles of soda used. Cadet Star now has 99.5 bottles of soda (5 * 24 – 20.5 = 120 – 20.5 = 99.5). He puts 3.5 of these aside and redistributes the other 96 to fill four cases completely. With one less case to move, Bu will now make 2 fewer trips. The 3.5 bottles set aside are used to move the four cases the next 1/2 mile towards the Wirth Pavilion. After this, the Wirth Pavilion is just miles away ( 5 – – 9/18 = ). Next, he travels miles (7 * ) using bottles of soda to complete his trip. The ranger cadet delivers 80 bottles to the pavilion and has of a Park Pop to spare. (96 – = 80 )
