3rd Kyū

Next, let's consider the anti-diagonals that run from top-left to bottom-right.

The starting point of an anti-diagonal is always a square on the a-file or the 8th rank.

Along an anti-diagonal, tracing up-left (↖) decreases the file and increases the rank, so it reaches either the a-file (left edge) or the 8th rank (top edge) first.

The steps to the a-file is "file value - 1", and the steps to the 8th rank is "8 - rank value". The smaller value determines which edge is reached first.

For example, consider a bishop on c3. Steps to the a-file: 3 - 1 = 2, steps to the 8th rank: 8 - 3 = 5.

The a-file is reached first, so adding 2 to the rank gives 3 + 2 = 5, and the starting point is a5.

Conversely, for a bishop on f7, steps to the a-file: 6 - 1 = 5, steps to the 8th rank: 8 - 7 = 1.

The 8th rank is reached first, so subtracting 1 from the file gives 6 - 1 = 5, and the starting point is e8.

When both step counts are equal, the starting point is always a8. This is the a8-h1 main anti-diagonal.