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Omni-MATH / A collection of n squares on the plane is called tri-connected if the following criteria are satisfied: (i) All the squares are congruent. (ii) If two squares have a point P in com…

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problem

A collection of nn squares on the plane is called tri-connected if the following criteria are satisfied: (i) All the squares are congruent. (ii) If two squares have a point PP in common, then PP is a vertex of each of the squares. (iii) Each square touches exactly three other squares. How many positive integers nn are there with 2018≤n≤30182018 \leq n \leq 3018, such that there exists a collection of nn squares that is tri-connected?
Plain-text mathematical notation (without MathML)
A collection of n squares on the plane is called tri-connected if the following criteria are satisfied: (i) All the squares are congruent. (ii) If two squares have a point P in common, then P is a vertex of each of the squares. (iii) Each square touches exactly three other squares. How many positive integers n are there with 2018≤n≤3018, such that there exists a collection of n squares that is tri-connected?
Original LaTeX notation
A collection of $n$ squares on the plane is called tri-connected if the following criteria are satisfied: (i) All the squares are congruent. (ii) If two squares have a point $P$ in common, then $P$ is a vertex of each of the squares. (iii) Each square touches exactly three other squares. How many positive integers $n$ are there with $2018 \leq n \leq 3018$, such that there exists a collection of $n$ squares that is tri-connected?

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task_id
f4d05d0c-87dd-5d0e-bdf4-136270574649
task_key
test--f4d05d0c-87dd-5d0e-bdf4-136270574649
task_revision_id
1
config / split
/ test

Official source

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