POTW #11 - March 10, 2024
Contributed by: devourer
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Difficulty: 9
This problem is tagged with potw, potw2024, devourer.
MCR Problem of the Week, March 10, 2024 Edition
$5$ pirates, $A$, $B$, $C$, $D$, and $E$, looted $100$ gold coins and they will use this process to divide the coins among themselves:
- Pirate $A$ proposes a plan to divide the coins, such as $60$, $10$, $10$, $10$, and $10$
- All pirates vote "Yes" or "No" after hearing the plan. The pirate who proposed the plan also votes and no one can remain neutral
- If strictly greater than 50% of votes are "Yes", the plan passes and is implemented. Otherwise, the pirate who proposed the plan is killed and the next pirate (in this case, $B$) starts over from step $1$
- Stay alive
- Get as many gold coins as possible
- Kill as many other pirates as possible
How many gold coins can pirate $A$ get?
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