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Omni-MATH / Sammy has a wooden board, shaped as a rectangle with length 2²⁰¹⁴ and height 3²⁰¹⁴. The board is divided into a grid of unit squares. A termite starts at either the left or bottom …

Problem

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problem

Sammy has a wooden board, shaped as a rectangle with length 220142^{2014} and height 320143^{2014}. The board is divided into a grid of unit squares. A termite starts at either the left or bottom edge of the rectangle, and walks along the gridlines by moving either to the right or upwards, until it reaches an edge opposite the one from which the termite started. The termite's path dissects the board into two parts. Sammy is surprised to find that he can still arrange the pieces to form a new rectangle not congruent to the original rectangle. This rectangle has perimeter PP. How many possible values of PP are there?
Plain-text mathematical notation (without MathML)
Sammy has a wooden board, shaped as a rectangle with length 2²⁰¹⁴ and height 3²⁰¹⁴. The board is divided into a grid of unit squares. A termite starts at either the left or bottom edge of the rectangle, and walks along the gridlines by moving either to the right or upwards, until it reaches an edge opposite the one from which the termite started. The termite's path dissects the board into two parts. Sammy is surprised to find that he can still arrange the pieces to form a new rectangle not congruent to the original rectangle. This rectangle has perimeter P. How many possible values of P are there?
Original LaTeX notation
Sammy has a wooden board, shaped as a rectangle with length $2^{2014}$ and height $3^{2014}$. The board is divided into a grid of unit squares. A termite starts at either the left or bottom edge of the rectangle, and walks along the gridlines by moving either to the right or upwards, until it reaches an edge opposite the one from which the termite started. The termite's path dissects the board into two parts. Sammy is surprised to find that he can still arrange the pieces to form a new rectangle not congruent to the original rectangle. This rectangle has perimeter $P$. How many possible values of $P$ are there?

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Source and history

task_id
44ac82c5-d9c3-542d-bacf-c5a80f0fbd09
task_key
test--44ac82c5-d9c3-542d-bacf-c5a80f0fbd09
task_revision_id
1
config / split
/ test

Official source

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