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Omni-MATH / For an integer m≥1, we consider partitions of a 2^(m)×2^(m) chessboard into rectangles consisting of cells of chessboard, in which each of the 2^(m) cells along one diagonal forms …

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problem

For an integer m≥1m\geq 1, we consider partitions of a 2m×2m2^m\times 2^m chessboard into rectangles consisting of cells of chessboard, in which each of the 2m2^m cells along one diagonal forms a separate rectangle of side length 11. Determine the smallest possible sum of rectangle perimeters in such a partition. [i]
Plain-text mathematical notation (without MathML)
For an integer m≥1, we consider partitions of a 2^(m)×2^(m) chessboard into rectangles consisting of cells of chessboard, in which each of the 2^(m) cells along one diagonal forms a separate rectangle of side length 1. Determine the smallest possible sum of rectangle perimeters in such a partition.

[i]
Original LaTeX notation
For an integer $m\geq 1$, we consider partitions of a $2^m\times 2^m$ chessboard into rectangles consisting of cells of chessboard, in which each of the $2^m$ cells along one diagonal forms a separate rectangle of side length $1$. Determine the smallest possible sum of rectangle perimeters in such a partition.

[i]

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task_id
98f7b7b1-3eac-545d-84e8-06139b58ab2a
task_key
test--98f7b7b1-3eac-545d-84e8-06139b58ab2a
task_revision_id
1
config / split
/ test

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