Solution to Saturn Puzzler

In order to denote the equations, eight symbols are defined as N, NE, E, SE, SW, W, NW and W as shown below.

N represents flipping the upper half about the N-S axis, E represents flipping the half on the right about the E-W axis, and so.

An equation is expressed as the following format:

(a, n) x1, x2, ..., xn

where a is the number of pieces relocated by the equation, n is the number of steps, and xi are the n steps for i = 1, 2, ..., n.

For example, to move the piece M anti-clockwise by 4 slots, the equation is

(6,2) S, E

A represents the piece(s) not to be affected by the equation.

M represents the piece to be relocated by the equation.

The complete solution is as follows:

 

(5, 3) E, SE, E

 

(5, 2) SE, E

 

(4, 1) E

 

(6, 2) S, E

 

(5, 4) SE, E, SE, E

 

(4, 10) E, N, NE, N, W, SW, W, SE, S, SE

 

(3, 9) N, NE, N, W, SW, W, SE, S, SE

 

(2, 11) NW, W, NW, NE, E, S, SW, S, NW, W, NW