Library / Belarusian Mathematical Olympiad /34 of 208

Belarusian Mathematical Olympiad

Combinatorics Difficulty 5.3 AIME, harder Prove it Belarus

Each cell of an $n \times n$ table is filled with one of the two signs: «+» and «-». For each $k$ from $1$ to $n$ the amount of pluses in the first $k$ rows is greater than the amount of minuses in the first $k$ columns.
Find the maximal possible number of minuses in the table.

Solution

Answer: $\left[ \frac{n^2 - 1}{2} \right]$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.