3,000 bananas, a 1,000km desert, and a camel that eats as it walks
A trader has 3,000 bananas at one edge of a 1,000km desert and a camel that can carry at most 1,000 bananas at a time — but eats one banana per kilometre travelled, loaded or not. The camel can make as many back-and-forth trips as needed, dropping banana caches along the way. What's the largest number of bananas that can reach the far side?
Reveal the answer
533 bananas. The trick is multiple relay trips: with 3,000 bananas you need 5 loads to shift the first stretch (burning 4 extra trips' worth of fuel), dropping to 3 trips once you're under 2,000, then 1 trip once under 1,000 — each threshold changes the effective 'cost per kilometre' of moving the pile forward. It's a version of the mathematical 'jeep problem,' first analyzed rigorously in 1947.
— N. J. Fine, Jeep problem — American Mathematical Monthly, 1947