An explorer undertakes to cross a desert with the help of porters. The length of the trail corresponds to 6 days walk. But the explorer, like each porter, can carry only 4 days food. How many porters does the explorer need? In fact, can he cross at all?
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The explorer can cross the desert using only two porters. They all leave one morning, each with 4 days food. At the end of the first day, each has 3 days food left. The first porter goes back with one days food, leaving 4 days food each for the explorer and the second porter. At the end of the second day, the two men each have 3 days food. The second porter goes back with 2 days food. The explorer goes on with 4 days food, enough to reach his goal.
The engineering department was arranging for a rather expensive catered lunch to bid farewell to their retiring colleague. They calculated that it would cost each person $30. One good mathematician remarked, "It's lucky that there aren't five fewer of us to split the...