Exploring The Desert
Nine travellers, each possessing a car, meet on the eastern edge of a desert. They wish to explore the interior, always going due west. Each car can travel forty miles on the contents of the engine tank, which holds a gallon of fuel, and each can carry nine extra gallon cans of fuel and no more. Unopened cans can alone be transferred from car to car. What is the greatest distance at which they can enter the desert without making any depots of fuel for the return journey?
The nine men, A, B, C, D, E, F, G, H, J, all go 40 miles together on the I gal. in their engine tanks, when A transfers I gal. to each of the other eight and has I gal. left to return home. The eight go another 40 miles, when B transfers I gal. to each of the other seven and has 2 gals. to take him home. The seven go another 40 miles, when C transfers I gal. to each ofthe six others and returns home on the remaining 3 gals. The six go another 40 miles, when D gives each of five I gal. and returns home. The five go 40 miles, when E gives each of four I gal. and returns home. The four go another 40 miles, when F gives each of three I gal. and returns home. The three go 40 miles, when G gives each of two I gal. and returns home. The two go 40 miles, when H gives I gal. to J and returns home. Finally, the last man, J, goes another 40 miles and then has 9 gals. to take him home. Thus J has gone 360 miles out and home, the greatest distance in a straight line that could be reached under the conditions.
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