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Omni-MATH / Five people are at a party. Each pair of them are friends, enemies, or frenemies…

Problem

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problem

Five people are at a party. Each pair of them are friends, enemies, or frenemies (which is equivalent to being both friends and enemies). It is known that given any three people A,B,CA, B, C : - If AA and BB are friends and BB and CC are friends, then AA and CC are friends; - If AA and BB are enemies and BB and CC are enemies, then AA and CC are friends; - If AA and BB are friends and BB and CC are enemies, then AA and CC are enemies. How many possible relationship configurations are there among the five people?
Plain-text mathematical notation (without MathML)
Five people are at a party. Each pair of them are friends, enemies, or frenemies (which is equivalent to being both friends and enemies). It is known that given any three people A,B,C : - If A and B are friends and B and C are friends, then A and C are friends; - If A and B are enemies and B and C are enemies, then A and C are friends; - If A and B are friends and B and C are enemies, then A and C are enemies. How many possible relationship configurations are there among the five people?
Original LaTeX notation
Five people are at a party. Each pair of them are friends, enemies, or frenemies (which is equivalent to being both friends and enemies). It is known that given any three people $A, B, C$ : - If $A$ and $B$ are friends and $B$ and $C$ are friends, then $A$ and $C$ are friends; - If $A$ and $B$ are enemies and $B$ and $C$ are enemies, then $A$ and $C$ are friends; - If $A$ and $B$ are friends and $B$ and $C$ are enemies, then $A$ and $C$ are enemies. How many possible relationship configurations are there among the five people?

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Source and history

task_id
76ff9ce6-5d75-5fa0-a723-a1541435ea1d
task_key
test--76ff9ce6-5d75-5fa0-a723-a1541435ea1d
task_revision_id
1
config / split
/ test

Official source

initial import