# Seven Impatient Knights

Source

On a $3\times3$ chess board, you must place seven knights according to the following rules:

1. Immediately after placement, the knight must move to an unoccupied spot using a standard knight's move.
2. Any placement where an immediate move is not possible is considered invalid.
3. After being placed and moved once, the knight can never move again.

As an example, if your first placement is at A1, the knight must immediately move to either B3 or C2.

Find a series of placements and moves that allow you to place all seven knights.

The trick is to place them

so they move into the previously placed spot. That way, you know there'll always be a spot open.

Full list:

A1→B3, C2→A1, A3→C2, B1→A3, C3→B1, A2→C3, C1→A2

Place on A1 --> B3 Place on C2 --> A1 Place on A3 --> C2 Place on B1 --> A3 Place on C3 --> B1 Place on A2 --> C3 Place on C1 --> A2

Remarks:

A knight can never be placed on B2 since it has nowhere to go. Considering the other 8 squares, we can construct a graph from knight moves, which we can unfold to reveal the answer.