Friday puzzle: bananas

Last week’s puzzle was to estimate when the 20th record year of rainfall will occur in New York. The answer is in 272 million years time. In 1835 that year was a record year by definition. In 1836 there were two equally likely combinations: two record years in 1835 and 1836; or record in 1835 but not a record in 1836. Since those two outcomes contain 3 records the expected number of records is 3/2 or 1.5. The chance that 1837 is a record year is 1/3 (one of the three years has to be the biggest and it is equally likely to be any of them).  By similar reasoning, the expected number of record years at that point is 1 + ½ + 1/3. In fact the expected number of record years in year N is just 1 + ½ + 1/3 +… 1/N. You might even remember from math class that this is called the Nth harmonic number and you might further remember that although it grows unboundedly large it grows incredibly slowly. In fact so slowly that it takes hundreds of millions of years to get to 20.

Now for today’s problem. A banana plantation is located next to a desert. The plantation owner has 3000 bananas. The market is 1000 kilometers away. He has one camel which can carry a maximum of 1000 bananas at a time but eats one banana for every kilometer it travels. How do you get the maximum number of bananas to market?

Answer next week.

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