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Omni-MATH / Two players play alternately on a 5×5 board. The first player always enters a 1 into an empty square and the second player always enters a 0 into an empty square. When the board is…

Problem

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problem

Two players play alternately on a 5×5 5 \times 5 board. The first player always enters a 1 1 into an empty square and the second player always enters a 0 0 into an empty square. When the board is full, the sum of the numbers in each of the nine 3×3 3 \times 3 squares is calculated and the first player's score is the largest such sum. What is the largest score the first player can make, regardless of the responses of the second player?
Plain-text mathematical notation (without MathML)
Two players play alternately on a 5×5 board. The first player always enters a 1 into an empty square and the second player always enters a 0 into an empty square. When the board is full, the sum of the numbers in each of the nine 3×3 squares is calculated and the first player's score is the largest such sum. What is the largest score the first player can make, regardless of the responses of the second player?
Original LaTeX notation
Two players play alternately on a $ 5 \times 5$ board. The first player always enters a $ 1$ into an empty square and the second player always enters a $ 0$ into an empty square. When the board is full, the sum of the numbers in each of the nine $ 3 \times 3$ squares is calculated and the first player's score is the largest such sum. What is the largest score the first player can make, regardless of the responses of the second player?

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Source and history

task_id
7cc96908-321d-54d6-8bcc-b919a5e267e9
task_key
test--7cc96908-321d-54d6-8bcc-b919a5e267e9
task_revision_id
1
config / split
/ test

Official source

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