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Desert crossing puzzle: the minimum fuel problem [1]

['Mark Frauenfelder']

Date: 2025-09-17

A puzzle from More Problematic Recreations, published by Litton Industries in the early 1960s:

A truck, when fully loaded, can carry enough fuel to take it half-way across a barren desert. If the truck can return to its starting point as often as is necessary, what is the minimum amount of fuel required to take it all the way across? Assume that any amount of fuel can be taken from the truck at any point in the desert and this amount will remain undiminished until subsequently collected.

If you drive halfway across the desert, you will run out of fuel and get stuck there. If you drive one quarter of the way, you'll have just enough fuel to return. So, there is some point between the beginning and driving one-quarter into the desert where you should drop some fuel off and then return and refill the truck. But where? And what about the next trip? Where do you stop and when do you use the fuel you dropped off?

Three Problematic Recreation booklets have been uploaded to the Internet Archive.

Litton Industries, was a large defense contractor that was acquired by Northrop Grumman in 1980 for $5 billion. It published at least eight Problematic Recreation booklets, all in the early to mid-1960s. Three are available on the Internet Archive.

The Archive also has a scan of a book called Mathematical Bafflers: A collection of the best puzzles from the famous Problematical Recreations series of Litton Industries. Published in 1964, it contains a few puzzles that reveal the casual racism and misogyny of the time. Scientists and professionals are always depicted as white men, and women are often objectified. Here's an example:

Previously:

• Fountain puzzle: Connect water to houses without crossing pipes

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