1

Part of 2009 Kurschak Competition

Problems(1)

Permutations of 1,2,..,k in the rows of an array

Source: Kürschak 2009, problem 1

n,k

be arbitrary positive integers. We fill the entries of an

n\times k

array with integers such that all the

n

rows contain the integers

1,2,\dots,k

in some order. Add up the numbers in all

k

columns – let

S

be the largest of these sums. What is the minimal value of

S

combinatorics unsolvedcombinatorics