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OlympiadBench / 2037 / Queenie and Horst play a game on a 20×20 chessboard. In the beginning…

Problem

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question

Queenie and Horst play a game on a

20 \times 20

chessboard. In the beginning the board is empty. In every turn, Horst places a black knight on an empty square in such a way that his new knight does not attack any previous knights. Then Queenie places a white queen on an empty square. The game gets finished when somebody cannot move. Find the maximal positive

K

such that, regardless of the strategy of Queenie, Horst can put at least

K

knights on the board.

Plain-text mathematical notation (without MathML)

Queenie and Horst play a game on a 20×20 chessboard. In the beginning the board is empty. In every turn, Horst places a black knight on an empty square in such a way that his new knight does not attack any previous knights. Then Queenie places a white queen on an empty square. The game gets finished when somebody cannot move.

Find the maximal positive K such that, regardless of the strategy of Queenie, Horst can put at least K knights on the board.

Original LaTeX notation

Queenie and Horst play a game on a $20 \times 20$ chessboard. In the beginning the board is empty. In every turn, Horst places a black knight on an empty square in such a way that his new knight does not attack any previous knights. Then Queenie places a white queen on an empty square. The game gets finished when somebody cannot move.

Find the maximal positive $K$ such that, regardless of the strategy of Queenie, Horst can put at least $K$ knights on the board.

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2037
task_id: f05a89c3-0b52-5f70-aded-dfd825769f8f
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2037
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

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