Efficient Knight Cover Patterns Part II
The Knight Spillage Puzzle

Preface
Part I examined efficient knight cover patterns on the infinite plane
with the aim of using them in the center of large finite boards.
Part II examines efficient edge patterns.

Part I eased the task of finding efficient patterns by modifying the knight cover puzzle
into one which addressed the problem more directly.
In Part II, we do this again.

Introduction
The most efficient central patterns don't fit on the edge as well as some less efficient central patterns.
The difference is enough so that on small boards,
the most efficient patterns are generally not used.
So larger boards would have to be examined to find out
what efficient edges look like.
As an alternative to this,
define a new puzzle that uses these patterns on smaller boards.

[ Find efficient edge patterns.]
[Find efficient transitions from the edge to the Monier isometries.]
[Determine the size of the board where Monier isometries
are always required for optimal solutions].

The Knight Cover Spillage Puzzle
If we put one of the edges back for the Knight Over-Coverage Puzzle,
we get the Knight Cover Spillage Puzzle.

We have an 8x8 board in the center of a 12x12 area of squares.
We need to cover all the squares of the 8x8 board.
We can place knights either on the 8x8 board or outside
except for the top two rows.
These rows are squares that are beyond the edge of the 8x8 board
and therefore can't be occupied.

The puzzle is to place knights that cover the 8x8 board
while minimizing the sum of over-coverage within the 8x8 board
and spillage in the top two rows.