RU-ALLRUSSIAN 1991 Problem 15

An $h \times k$ minor of an n x n table is the hk cells which lie in h rows and k columns. The semiperimeter of the minor is $\mathrm{h} + \mathrm{k}$ . A number of minors each with semiperimeter at least n together include all the cells on the main diagonal. Show that they include at least half the cells in the table.