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OlympiadBench / 2230 / Let k be a positive integer. Lexi has a dictionary D consisting of…

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

k

be a positive integer. Lexi has a dictionary

\mathcal{D}

consisting of some

k

-letter strings containing only the letters

A

and

B

. Lexi would like to write either the letter

A

or the letter

B

in each cell of a

k \times k

grid so that each column contains a string from

\mathcal{D}

when read from top-to-bottom and each row contains a string from

\mathcal{D}

when read from left-to-right. What is the smallest integer

m

such that if

\mathcal{D}

contains at least

m

different strings, then Lexi can fill her grid in this manner, no matter what strings are in

\mathcal{D}

Plain-text mathematical notation (without MathML)

Let k be a positive integer. Lexi has a dictionary D consisting of some k-letter strings containing only the letters A and B. Lexi would like to write either the letter A or the letter B in each cell of a k×k grid so that each column contains a string from D when read from top-to-bottom and each row contains a string from D when read from left-to-right.

What is the smallest integer m such that if D contains at least m different strings, then Lexi can fill her grid in this manner, no matter what strings are in D ?

Original LaTeX notation

Let $k$ be a positive integer. Lexi has a dictionary $\mathcal{D}$ consisting of some $k$-letter strings containing only the letters $A$ and $B$. Lexi would like to write either the letter $A$ or the letter $B$ in each cell of a $k \times k$ grid so that each column contains a string from $\mathcal{D}$ when read from top-to-bottom and each row contains a string from $\mathcal{D}$ when read from left-to-right.

What is the smallest integer $m$ such that if $\mathcal{D}$ contains at least $m$ different strings, then Lexi can fill her grid in this manner, no matter what strings are in $\mathcal{D}$ ?

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2230
task_id: 6ede16e3-a89c-550e-bef3-a27662d4cb41
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2230
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import