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A group of 100 friends stands in a circle. Initially, one person has 2019 mangos, and no one else has mangos. The friends split the mangos according to the following rules:

 

• sharing: to share, a friend passes two mangos to the left and one mango to the right.

• eating: the mangos must also be eaten and enjoyed. However, no friend wants to be selfish and eat too many mangos. Every time a person eats a mango, they must also pass another mango to the right.

 

A person may only share if they have at least three mangos, and they may only eat if they have at least two mangos. The friends continue sharing and eating, until so many mangos have been eaten that no one is able to share or eat anymore. Show that there are exactly eight people stuck with mangos, which can no longer be shared or eaten.

 Oct 4, 2019
 #1
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Ugh....I hate mangos....I do not 'do' mango problems....good luck....   ~EP cheeky

 Oct 4, 2019
 #2
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I love mangos but i have no idea how to solve your problem.    sad

 

If you get the answer, please share it with us.   laugh

 Oct 4, 2019
edited by Melody  Oct 4, 2019
 #3
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Not quite sure how to solve this either, but after writing out a couple of steps, there seem to be some patterns in  the number of mangoes different people have... Not sure about a proof yet though. Would really appreciate it if someone more knowledgeable could look at this! 

 Oct 4, 2019
 #4
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Don't respond to this question. This is from an ongoing math competition not from homework. 

 Oct 6, 2019
 #5
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This is from an ongoing competition and discussion of this problem is not permitted until the due date has passed.

 

https://www.usamts.org/

 

Please be aware that by answering this, you will be cheating/assisting someone to cheat. If anyone knows how to report questions, please do so.

 Oct 6, 2019
 #6
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Thanks for letting us know.  I can block further answers without deleting the question.

I would really be interested in seeing the answer once the competition is over. 

Melody  Oct 6, 2019

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