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Omni-MATH / The country Dreamland consists of 2016 cities. The airline Starways wants to…
Problem
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problem
The country Dreamland consists of 2016 cities. The airline Starways wants to establish some one-way flights between pairs of cities in such a way that each city has exactly one flight out of it. Find the smallest positive integer such that no matter how Starways establishes its flights, the cities can always be partitioned into groups so that from any city it is not possible to reach another city in the same group by using at most 28 flights.
Plain-text mathematical notation (without MathML)
The country Dreamland consists of 2016 cities. The airline Starways wants to establish some one-way flights between pairs of cities in such a way that each city has exactly one flight out of it. Find the smallest positive integer k such that no matter how Starways establishes its flights, the cities can always be partitioned into k groups so that from any city it is not possible to reach another city in the same group by using at most 28 flights.
Original LaTeX notation
The country Dreamland consists of 2016 cities. The airline Starways wants to establish some one-way flights between pairs of cities in such a way that each city has exactly one flight out of it. Find the smallest positive integer $k$ such that no matter how Starways establishes its flights, the cities can always be partitioned into $k$ groups so that from any city it is not possible to reach another city in the same group by using at most 28 flights.
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Source and history
- task_id
016a2013-be1c-5fff-b6df-c06cb455d127- task_key
test--016a2013-be1c-5fff-b6df-c06cb455d127- task_revision_id
- 1
- config / split
- / test
initial import