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banana theves


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This riddle is a bit long but a very good one.

My grandpa used to tell it all the time.

There were three robbers with a pet monkey. One evening they stole a large bunch of bananas. They got home rather late and decided to go to bed and split the bananas up in the morning. In the middle of the night the first robber wakes up and realizes that the other two men can’t be trusted seeing they are robbers. He therefore decides to divide the bananas then by himself. When he divides the bunch in three there is one left over so he gives it to the monkey. He hides his 1/3, puts the other 2/3 back, and goes back to sleep. Not long after the second robber wakes up and similarly realizes his colleagues can’t be trusted. He takes the bananas out and divides them in 3rds, there is one left over so he gives it to the monkey. He hides his 1/3, puts the other 2/3 back, and goes back to sleep. It isn’t much later that the third robber awakens with the realization that his friends are not to be trusted. He also takes the bananas out and divides them in 3rds, there is again one left over so he gives it to the monkey. He hides his 1/3, puts the other 2/3 back, and goes back to sleep. In the morning the three robbers wake up, each can easily see that the banana bunch has greatly diminished, but not wanting to admit to his own activities during the night says nothing. They divide the remaining bananas evenly and surprisingly enough there is still one banana left over for the monkey.

What is the fewest number of bananas that they could have stolen for this to work out and have the described division of bananas without ever cutting up bananas?

there were 79 bananas (((((((79-1)*2/3)-1)*2/3)-1)*2/3)-1)/3=7 the next solution doesnt work till 160 just over double the bananas

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Start with 79 bananas. 79 = 3x26 + 1. First theif takes 26, leaves 52, gives 1 to the monkey

Now there's 52 bananas. 52 = 3x17 + 1. Second theif takes 17, leaves 34, gvies 1 to the monkey

Now there's 34 bananas. 34 = 3x11 + 1. Third thief takes 11 , leaves 22, gives 1 to the monkey.

Now there's 22 bananas. 22 = 3x7 + 1. The three thieves each take 7, and give 1 to the monkey.

There can't be fewer than 7 in the last division, else bananas would have to have been split earlier.

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