Chess piece called [i]skew knight[/i], if placed on the black square, attacks all the gray squares. 

[img]https://i.ibb.co/HdTDNjN/Kyiv-MO-2021-Round-1-11-2.png[/img]

What is the largest number of such knights that can be placed on the $8\times 8$ chessboard without them attacking each other?

[i]Proposed by Arsenii Nikolaiev[/i]
1. **Understanding the Problem:**
   - A skew knight placed on a black square attacks all the gray squares.
   - We need to find the maximum number of skew knights that can be placed on an $8 \times 8$ chessboard such that no two knights attack each other.

2. **Analyzing the Chessboard:**
   - An $8 \times 8$ chessboard has 64 squares.
   - The squares are alternately colored black and white.
   - There are 32 black squares and 32 white squares on the chessboard.

3. **Placement Strategy:**
   - If a skew knight is placed on a black square, it attacks all the gray squares.
   - Therefore, if we place knights only on black squares, they will not attack each other because they only attack gray squares.

4. **Maximizing the Number of Knights:**
   - Since there are 32 black squares on the chessboard, we can place one knight on each black square.
   - This ensures that no two knights attack each other, as they are all on black squares and only attack gray squares.

5. **Conclusion:**
   - The maximum number of skew knights that can be placed on the chessboard without them attacking each other is 32.

The final answer is $\boxed{32}$