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Omni-MATH / Consider a 2n×2n board. From the i th line we remove the central 2(i−1) unit squares. What is the maximal number of rectangles 2×1 and 1×2 that can be placed on the obtained figure…

Problem

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problem

Consider a

2n \times 2n

board. From the

i

th line we remove the central

2(i-1)

unit squares. What is the maximal number of rectangles

2 \times 1

and

1 \times 2

that can be placed on the obtained figure without overlapping or getting outside the board?

Plain-text mathematical notation (without MathML)

Consider a 2n×2n board. From the i th line we remove the central 2(i−1) unit squares. What is the maximal number of rectangles 2×1 and 1×2 that can be placed on the obtained figure without overlapping or getting outside the board?

Original LaTeX notation

Consider a $2n \times 2n$ board. From the $i$ th line we remove the central $2(i-1)$ unit squares. What is the maximal number of rectangles $2 \times 1$ and $1 \times 2$ that can be placed on the obtained figure without overlapping or getting outside the board?

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task_id: 672258b9-33eb-5028-923e-d9828313218f
task_key: test--672258b9-33eb-5028-923e-d9828313218f
task_revision_id: 3
config / split: / test

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