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Puzzles and Challenges / The Dominion Number
« on: September 16, 2012, 10:28:53 am »
We often ask challenges like this: Maximize/minimize n such that there is a kingdom k such that P(k,n).
This is a question of the form: Maximize/minimize n such that for all kingdoms k we have P(k,n).
As remarked by Donald, one of the most obvious choice for P is "A solo player in kingdom k can gain all Provinces in n turns."
Therefore, I ask: What is the minimal n such that a solo player can guarantee gaining all Provinces in n turns no matter what the kingdom?
This minimal n could be called "The Dominion Number" akin to God's Number for Rubik's Cube.
Clarifications:
This is a question of the form: Maximize/minimize n such that for all kingdoms k we have P(k,n).
As remarked by Donald, one of the most obvious choice for P is "A solo player in kingdom k can gain all Provinces in n turns."
Therefore, I ask: What is the minimal n such that a solo player can guarantee gaining all Provinces in n turns no matter what the kingdom?
This minimal n could be called "The Dominion Number" akin to God's Number for Rubik's Cube.
Clarifications:
- The shuffling is random.
- Extra turns like Outpost and Possession turns do not count (but I doubt it matters for the solution).
- Any Black Market deck is allowed (but I also doubt it matters).