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Omni-MATH / The cells of a 8×8 table are initially white. Alice and Bob play a game. First Alice paints n of the fields in red. Then Bob chooses 4 rows and 4 columns from the table and paints …

Problem

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problem

The cells of a 8×88 \times 8 table are initially white. Alice and Bob play a game. First Alice paints nn of the fields in red. Then Bob chooses 44 rows and 44 columns from the table and paints all fields in them in black. Alice wins if there is at least one red field left. Find the least value of nn such that Alice can win the game no matter how Bob plays.
Plain-text mathematical notation (without MathML)
The cells of a 8×8 table are initially white. Alice and Bob play a game. First Alice paints n of the fields in red. Then Bob chooses 4 rows and 4 columns from the table and paints all fields in them in black. Alice wins if there is at least one red field left. Find the least value of n such that Alice can win the game no matter how Bob plays.
Original LaTeX notation
The cells of a $8 \times 8$ table are initially white. Alice and Bob play a game. First Alice paints $n$ of the fields in red. Then Bob chooses $4$ rows and $4$ columns from the table and paints all fields in them in black. Alice wins if there is at least one red field left. Find the least value of $n$ such that Alice can win the game no matter how Bob plays.

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Source and history

task_id
a228e676-c739-5ddf-9afd-727cc0d88ab1
task_key
test--a228e676-c739-5ddf-9afd-727cc0d88ab1
task_revision_id
1
config / split
/ test

Official source

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