6

Part of 2010 South africa National Olympiad

Problems(1)

The largest minimum sum of entries in a table

Source: South African MO 2010 Q6

1

-1

in each of the cells of a

(2n) \times (2n)

-table, in such a way that there are exactly

2n^2

entries of each kind. Let the minimum of the absolute values of all row sums and all column sums be

M

. Determine the largest possible value of

M

combinatorics unsolvedcombinatorics