This is one of my favorites – I read this puzzle for the first time in 1992 on rec.puzzles (for those of you who remember these newsgroups!), and honestly have struggled with this ever since. I saw this puzzle again recently in one of the Martin Gardner books (more on sources when I send the answer). While the original puzzle is too tough for children, I have introduced a variant which the kids should be able to do.
An unlimited supply of Gasoline is available at one edge of a desert 800 miles wide, but there is no source on the desert itself. A truck can carry enough gasoline to go 600 miles (this will be called one “load”), and it can build up its own refueling stations at any spot along the way. These caches (i.e. gasoline storage) can be of any size, and it is assumed that there is no evaporation loss.
What is the minimum amount of Gasoline (in loads) the truck will require in order to cross the desert?
(i) In the previous version, change the size of the load to be enough to go for 500 miles and not 600 miles, and answer the same question.
(ii) Is there a limit to the width of a desert the truck can cross?
Source: My Best Mathematical and Logic Puzzles, by Martin Gardner, Puzzle #25
Please send the answers directly to me at firstname.lastname@example.org