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OlympiadBench / 1854 / Let n be a positive integer. Determine the smallest positive integer k with…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Expression

is multiple answer

false

language

English

question

Let

n

be a positive integer. Determine the smallest positive integer

k

with the following property: it is possible to mark

k

cells on a

2 n \times 2 n

board so that there exists a unique partition of the board into

1 \times 2

and

2 \times 1

dominoes, none of which contains two marked cells.

Plain-text mathematical notation (without MathML)

Let n be a positive integer. Determine the smallest positive integer k with the following property: it is possible to mark k cells on a 2n×2n board so that there exists a unique partition of the board into 1×2 and 2×1 dominoes, none of which contains two marked cells.

Original LaTeX notation

Let $n$ be a positive integer. Determine the smallest positive integer $k$ with the following property: it is possible to mark $k$ cells on a $2 n \times 2 n$ board so that there exists a unique partition of the board into $1 \times 2$ and $2 \times 1$ dominoes, none of which contains two marked cells.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1854
task_id: 0011c201-f74e-5d66-83b6-ff469a75c813
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1854
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import