05 December 2010

Chess mathematics

This time, I show some compositions for which you only need to know the following two things:
Here are some typical distances:
  • 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
  • knight-distance (e.g. g4—h2): √5
Before you continue reading, you may want to test yourself and see whether you can determine these distances correctly:
  • c5—f2 = ?
  • b3—e7 = ?
  • d2—d6 = ?
  • a5—h4 = ?

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.

  AAndreas Witt  
Die Welt, 1997
[8/2K4B/8/8/8/8/2P5R/8]
  (4+0)  
a) Diagram
b) wNc2

  BAndreas Witt  
Die Schwalbe, February 2010
[8/8/1P3R2/8/8/1Q3P2/8/8]
  (4+0)  
Zeroposition
a) wBf3
b) wNf3
c) wBb6
d) wNb6

  CAndreas Witt  
Die Schwalbe, April 2010
[8/2N4B/8/8/8/2Q4R/8/8]
  (4+0)  

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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