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:

  1. Pirate $A$ proposes a plan to divide the coins, such as $60$, $10$, $10$, $10$, and $10$
  2. All pirates vote "Yes" or "No" after hearing the plan. The pirate who proposed the plan also votes and no one can remain neutral
  3. 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 $1$
When deciding what to vote, all pirates follow this priority list:
  1. Stay alive
  2. Get as many gold coins as possible
  3. Kill as many other pirates as possible
Each pirate uses perfect logic and knows that the others will do the same.
How many gold coins can pirate $A$ get?

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