 the movement of the chess pieces
 calculation of the distance between two squares which is measured from the centre of each square making use of the Pythagorean theorem
 between two horizontally or vertically adjacent squares (e.g. a1—b1 or d7—d8): 1
 between two diagonally adjacent squares (e.g. e5—f6): √2, i.e. the square root of 2
 knightdistance (e.g. g4—h2): √5
Okay, now it's time for the puzzles. The stipulations are as follows:
Diagram A: The centers of the squares of the white pieces are the vertices of a square. How can you create a square of the same size somewhere else on the board by making 5 moves?
Diagram B: The centers of the squares of the white pieces are the vertices of a rectangle. Create a new rectangle with the same area somewhere else on the board by making 3 moves!
Remark: "Zeroposition" means that the diagram itself is not to be solved, but each position that is the result of the given change.
Diagram C: The centers of the squares of the white pieces are the vertices of a rectangle. White makes 4 moves, so that a new rectangle with the same area is created somewhere else on the board. There are 5 solutions.



Obviously, the move order in each solution is not important. Only the resulting arrangement of the pieces matters. Did you figure it all out?
A  a) 1. Kc8 2. Bf5 3. Rh8 4. Bh3 5. c3 b) 1. Kd8 2. Rh5 3. Ne1 4. Bc2 5. Ba4 
B  a) 1. Qb2 2. Re6 3. Be2 b) 1. Qb4 2. Rh6 3. Nh4 c) 1. Qc3 2. Rf7 3. Bc7 d) 1. Qd1 2. Rc6 3. Na4 
C  I) 1. Bd3 2. Bf1 3. Na6 4. Qc8 II) 1. Qh8 2. Bd3 3. Ne6 4. Nd8 III) 1. Qg7 2. Bc2 3. Rg3/Rh2 4. Rg2 IV) 1. Qb3 2. Rh5 3. Bg8 4. Na6 V) 1. Qc2 2. Rf3/Rh1 3. Rf1 4. Ne8 
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