4

Part of 2018 Mediterranean Mathematics OIympiad

Problems(1)

largest integer N, for which there exists a 6xN table, so that ...

Source: Mediterranean 2018 P4 MMC

Determine the largest integer

N

, for which there exists a

6\times N

T

that has the following properties:

*

Every column contains the numbers

1,2,\ldots,6

in some ordering.

*

For any two columns

i\ne j

, there exists a row

r

T(r,i)= T(r,j)

*

For any two columns

i\ne j

, there exists a row

s

T(s,i)\ne T(s,j)

.
(Proposed by Gerhard Woeginger, Austria)

combinatoricsnumbers in a tablemaximumMediterranean