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Week of September 20, 2010

posted Sep 12, 2010, 10:23 AM by George Jensen   [ updated Aug 1, 2011, 6:23 PM ]
Submit the solution to me (either on a piece of paper or in an e-mail to jeffmcq@gmail.com) by 8 p.m. on Sunday, September 26, and I'll bring you a specially-made baked good of your choice. Good luck! Here's this week's problem:

Five men crash-land their airplane on a deserted island in the South Pacific. On their first day they gather as many bananas as they can find into one big pile. They decide that, since it is getting dark, they will wait until the next day to divide the bananas.

That night each man took a turn watching for rescue searchers while the others slept. The first watcher got bored so he decided to divide the bananas into five equal piles. When he did this, he found he had one remaining banana. He gave this banana to a monkey, took one of the piles, and hid it for himself. Then he jumbled up the four other piles into one big pile again.

To cut a long story short, each of the five men ended up doing exactly the same thing. They each divided the bananas into five equal piles and had one extra banana left over, which they gave to the monkey. They each took one of the five piles and hid those bananas. They each came back and jumbled up the remaining four piles into one big pile.

What is the smallest number of bananas there could have been in the original pile?

This is a tough problem - remember you can't start off with fractions of a banana!
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