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2021 IMO Shortlist
C8
C8
Part of
2021 IMO Shortlist
Problems
(1)
Table of Permutations
Source: 2021 ISL C8
7/12/2022
Determine the largest integer
N
N
N
for which there exists a table
T
T
T
of integers with
N
N
N
rows and
100
100
100
columns that has the following properties:
(i)
\text{(i)}
(i)
Every row contains the numbers
1
1
1
,
2
2
2
,
…
\ldots
…
,
100
100
100
in some order.
(ii)
\text{(ii)}
(ii)
For any two distinct rows
r
r
r
and
s
s
s
, there is a column
c
c
c
such that
∣
T
(
r
,
c
)
−
T
(
s
,
c
)
∣
≥
2
|T(r,c) - T(s, c)|\geq 2
∣
T
(
r
,
c
)
−
T
(
s
,
c
)
∣
≥
2
. (Here
T
(
r
,
c
)
T(r,c)
T
(
r
,
c
)
is the entry in row
r
r
r
and column
c
c
c
.)
combinatorics