Rectangles $1\times20$, $1\times 19$, ..., $1\times 1$ were cut out of $20\times20$ table. Prove that the maximal amount of $1\times2$ dominos can be cut from the table is 85
Proposed by S. Berlov
Problem statement must be fixed;
At least 85 dominoes(1×2 rectangle) can be removed from the remainder.
Official solution can be found here. See Problem 8 in St.Petersburg section.
<Mathematical Olympiads 2001–2002; Problems and Solutions From Around the World>
In my opinion it was really hard problem...