Chess problem 3 by Christoph Bandelow

I thank Christoph Bandelow for allowing this chess problem, with a mathematical flavor, to be posted here.

 

Position:

  • In algebraic:White: King c7, Rooks c3 and d3, Knights b1 and e1,
    Pawn e3 (6 pieces).Black: King b5, Knight a4 and c4, Knights
    a4 and c4, Pawns a7, b6, and a5 (7 pieces).
  • In Forsyth notation:
    8
    p1K5
    rp6
    pk6
    n1n5
    2RRP3
    8
    1N2N3
    

From the chess problem collection “Problem-Juwelen” by Herbert Grasemann. Publisher: Siegfried Engelhardt Verlag, Berlin 1964.

bandelow_chess-problem3

White to mate in 6 (Christoph Bandelow, 1959)

 

 

 

 

 

 

 

 

 

Solution: 1. Rb3+ … 2. Rb5+ … 3. Rb3+ … 4. Rb5+ … 5. Nd3

 

This problem was originally posted at http://www.permutationpuzzles.org/chess/bandelow3.html.

 

 

Chess problem 2 by Christoph Bandelow

I thank Christoph Bandelow for allowing this chess problem, with a mathematical flavor, to be posted here.

 

Position:

  • In algebraic:White: King b4, Rooks b2 and e1, Bishop a1, Knight d4, Pawns c5, g3, g4
    (8 pieces).Black: King c1, Rook h1, Bishop d1, Knights d2 and g1, Pawns c6, d5,
    e2, g5, h2 (10 pieces).
  • In Forsyth notation:
    8
    8
    2p5
    2Pp2p1
    1K1N2P1
    6P1
    1R1np2p
    B1kbR1nr
    

From the chess problem collection “Problem-Juwelen” by Herbert Grasemann. Publisher: Siegfried Engelhardt Verlag, Berlin 1964.

bandelow_chess-problem2

White to mate in 8 (Christoph Bandelow, 1958)

 

 

 

 

 

Solution: 1. Kc3 Ne4+ 2. Kd3 Nf2+ 3. Ke3 Nxg4+ 4. Kd3 Nf2+ 5. Kc3 Ne4+ 6. Kb4 Nd2 7. g4

 

 

 

This problem was originally posted at http://www.permutationpuzzles.org/chess/bandelow2.html.

Chess problem 1 by Christoph Bandelow

I thank Christoph Bandelow for allowing this chess problem, with a mathematical flavor, to be posted here.

Position:

  • In algebraic:White: King g8, Queen e2, Bishops a1 and g4, Pawn e6 (5 pieces),Black: King f6, Bishop a2, Knight b1 (3 pieces).
  • In Forsyth notation:
    6K1
    8
    4Pk2
    8
    6B1
    8
    b3Q3
    Bn6

bandelow_chess-problem1

What were the last 6 single moves? (retrochess problem by Christoph Bandelow)

 

 

 

 

 

 

Solution: -1. d5xe6 e.p.+ -2. ….. d7-d5 -3. d4-d5+ -4. ….. Ke6xPf6+ -5. e6xf6 e.p.++ -6. ….. f7-f5

 

This problem was originally posted at http://www.permutationpuzzles.org/chess/bandelow1.html.

Mathematics of zombies

What do you do if there is a Zombie attack? Can mathematics help? This page is (humorously) dedicated to collecting links to papers or blog posted related to the mathematical models of Zombies.

 

George Romero’s 1968 Night of the Living Dead, now in the public domain, introduced reanimated ghouls, otherwise known as zombies, which craved live human flesh. Romero’s script was insired on Richard Matheson’s I Am Legend. In Romero’s version, the zombies could be killed by destroying the zombie’s brain. A dead human could, in some cases be “reanimated,” turning into a zombie. These conditions are modeled mathematically in several papers, given below.

  1. When Zombies Attack! Mathematical Modelling of a Zombie Outbreak!, paper by Mathematicians at the University of Ottawa, Philip Munz, Ioan Hudea, Joe Imad and Robert J. Smith? (yes, his last name is spelled “Smith?”).
  2. youtube video 28 Minutes Later – The Maths of Zombies , made by Dr James Grime (aka, “siningbanana”), which references the above paper.
  3. Epidemics in the presence of social attraction and repulsion, Oct 2010 Zombie paper by Evelyn Sander and Chad M. Topaz.
  4. Statistical Inference in a Zombie Outbreak Model, slides for a talk given by Des Higman, May 2010.
  5. Mathematics kills zombies dead!, 08/17/2009 blog post by “Zombie Research Society Staff”.
  6. The Mathematics of Zombies, August 18, 2009 blog post by Mike Elliot.
  7. Love, War and Zombies – Systems of Differential Equations using Sage, April 2011 slides by David Joyner. Sage commands for Love, War and Zombies talk. This was given as a Project Mosaic/M-cast broadcast.
  8. Public domain 1968 film Night of the Living Dead by George Romero.

Complements in the symmetric group

About 20 years ago I was asked a question of Herbert Kociemba, a computer scientist who has one of the best Rubik’s cube solving programs known. Efficient methods of storing permutations in S_E and S_V (the groups of all permutations of the edges E and vertices V, respectively, of the Rubik’s cube) are needed, hence leading naturally to the concept of the complement of S_m in S_n. Specifically, he asked if S_8 has a complement in S_{12} (this terminology is defined below). The answer is,
as we shall see, ”no.” Nonetheless, it turns out to be possible to introduce a slightly more general notion of a “k-tuple of complementary subgroups” (defined below) for which the answer to the analogous question is ”yes.”

This post is a very short summary of a paper I wrote (still unpublished) which can be downloaded here.