MathDB

Table of Permutations

Source: 2021 ISL C8

July 12, 2022

combinatorics

Problem Statement

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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