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Omni-MATH / What is the largest number of towns that can meet the following criteria. Each…

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problem

What is the largest number of towns that can meet the following criteria. Each pair is directly linked by just one of air, bus or train. At least one pair is linked by air, at least one pair by bus and at least one pair by train. No town has an air link, a bus link and a train link. No three towns, A,B,CA, B, C are such that the links between AB,ACAB, AC and BCBC are all air, all bus or all train.
Plain-text mathematical notation (without MathML)
What is the largest number of towns that can meet the following criteria. Each pair is directly linked by just one of air, bus or train. At least one pair is linked by air, at least one pair by bus and at least one pair by train. No town has an air link, a bus link and a train link. No three towns, A,B,C are such that the links between AB,AC and BC are all air, all bus or all train.
Original LaTeX notation
What is the largest number of towns that can meet the following criteria. Each pair is directly linked by just one of air, bus or train. At least one pair is linked by air, at least one pair by bus and at least one pair by train. No town has an air link, a bus link and a train link. No three towns, $A, B, C$ are such that the links between $AB, AC$ and $BC$ are all air, all bus or all train.

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Source and history

task_id
972a97b7-ff3c-57cf-96cc-4dc42ec80ee8
task_key
test--972a97b7-ff3c-57cf-96cc-4dc42ec80ee8
task_revision_id
1
config / split
/ test

Official source

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