Question 85
A $6 \times 6$ table is given.
a) If any 9 fields of the table are labeled, prove that it is possible to select three rows and three columns that contain all of the labeled fields.
b) Label 10 fields of the table so that for any three rows and three columns that we select there is at least one labeled field that is contained neither in the selected rows nor the columns.
(Moscow olympiad 1961, modified)
a) If any 9 fields of the table are labeled, prove that it is possible to select three rows and three columns that contain all of the labeled fields.
b) Label 10 fields of the table so that for any three rows and three columns that we select there is at least one labeled field that is contained neither in the selected rows nor the columns.
(Moscow olympiad 1961, modified)