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.

Guest Oct 4, 2019

#1**+1 **

Ugh....I hate mangos....I do not 'do' mango problems....good luck.... ~EP

ElectricPavlov Oct 4, 2019

#3**+1 **

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!

Guest Oct 4, 2019

#4**0 **

Don't respond to this question. This is from an ongoing math competition not from homework.

Guest Oct 6, 2019

#5**0 **

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.

Guest Oct 6, 2019