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Omni-MATH / Determine the largest integer N for which there exists a table T of integers with N rows and 100 columns that has the following properties: (i) Every row contains the numbers 1, 2,…

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problem

Determine the largest integer NN for which there exists a table TT of integers with NN rows and 100100 columns that has the following properties: (i)\text{(i)} Every row contains the numbers 11, 22, …\ldots, 100100 in some order. (ii)\text{(ii)} For any two distinct rows rr and ss, there is a column cc such that |T(r,c)−T(s,c)|≥2|T(r,c) - T(s, c)|\geq 2. (Here T(r,c)T(r,c) is the entry in row rr and column cc.)
Plain-text mathematical notation (without MathML)
Determine the largest integer N for which there exists a table T of integers with N rows and 100 columns that has the following properties:
(i) Every row contains the numbers 1, 2, …, 100 in some order.
(ii) For any two distinct rows r and s, there is a column c such that |T(r,c)−T(s,c)|≥2. (Here T(r,c) is the entry in row r and column c.)
Original LaTeX notation
Determine the largest integer $N$ for which there exists a table $T$ of integers with $N$ rows and $100$ columns that has the following properties:
$\text{(i)}$ Every row contains the numbers $1$, $2$, $\ldots$, $100$ in some order.
$\text{(ii)}$ For any two distinct rows $r$ and $s$, there is a column $c$ such that $|T(r,c) - T(s, c)|\geq 2$. (Here $T(r,c)$ is the entry in row $r$ and column $c$.)

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Source and history

task_id
eae0435b-f1d2-5ecf-882b-750bc4a4fb3c
task_key
test--eae0435b-f1d2-5ecf-882b-750bc4a4fb3c
task_revision_id
1
config / split
/ test

Official source

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