Ponder This Challenge - September 2017 - Fischer’s Fool’s Mate

Ponder This Challenge:

This month's challenge was suggested to us by Merse E. Gáspár from Hungary (thanks!)

Fischer Random Chess (also known as Chess960; see https://en.wikipedia.org/wiki/Chess960) is a version of chess designed by Bobby Fischer, the former world chess champion, in 1996. It uses the standard chess board and pieces, but it randomizes the starting positions of the pieces on the first home rank. Just as in standard chess, the white pawns are placed on the second rank, while all the remaining white pieces are placed randomly on the first rank, with two restrictions. The bishops must occupy squares of opposite colors. 2. The king must occupy a square between the two rooks. Black's pieces are placed equal-and-opposite to White's pieces.

Fool's Mate (see https://en.wikipedia.org/wiki/Fool%27s_mate), which is also called "Two-Move Checkmate", refers to checkmate achieved in the fewest possible number of moves from the start of the game. In standard chess, Fool's Mate can only be achieved by Black on move 2 with the queen. The rare checkmate is so named because it only take place if White is playing extraordinarily poorly.

Problem: How many of the 960 different Fischer variations mentioned above have the possibility of allowing a kind of Fool's Mate, or the shortest possible checkmate carried out by Black in just two steps?

Solution

• Click here to view the solution

  We present here Tom Harley's solution:

  There are 92 solutions.

  48 valid Chess960 initial white back rank positions are given below. Another 44 reverse the order of all 8 pieces. The last 4 cannot be reversed because queen-side castling has left-right asymmetry.

  1) RQKBNRBN  1. d3 c6 2. e4 Qf4#  
    
  2) RBKRNQBN  1. b3 e6 2. h3 Qa3# 
  3) RBKRBQNN 
   
  4) QBRKBNRN  1. e3 b6 2. g3 Qf3# 
   
  5) RNBKRNQB  1. c3 f6 2. a3 Qb3# 
  6) RNBKRBQN
   
  7) NRQKBNRB  1. e3 d6 2. f4 Qg4#
  8) RNQKBNRB   
  9) RBQKBNRN
   
  10) RNBKQNRB  1. c3 d6 2. b4 Qa4# 
  11) RNBKQBNR 
  12) RNBKQRNB   
  13) RNBKQBRN
   
  14) RKRNNQBB  1. b4 e6 2. Kb2 Qxb4#
  15) RKRNBQNB
  16) RKRBNQBN
  17) RKRBBQNN
  18) RKBNNQRB
  19) RKBNRQNB
  20) RKBRNQNB
  21) RKBBNQNR
  22) RKBBNQRN
  23) RKBBRQNN
   
  24) NRKRBNQB  1. c4 f6 2. Kc2 Qxc4#
  25) NRKRBBQN   
  26) BRKRNNQB  
  27) BRKRNBQN
  28) NRKBBNQR
  29) NRKBBRQN
  30) BRKBNNQR
  31) BRKBNRQN
  32) BRKBRNQN
  33) RBKRBNQN
   
  34) NNRKRBBQ  1. d4 g6 2. Kd2 Qxd4#
  35) NBRKRNBQ
  36) BNRKRBNQ
  37) BBRKRNNQ
  38) NNRKBBRQ
  39) NBRKBNRQ
  40) NBRKBRNQ
  41) RBBKRNNQ
  42) RNBKRBNQ
  43) NRBKRBNQ
   
  44) RKRBQNBN  1. b4 d6 2. b5 Qxb5#
   
  45) NBRKBQNR  1. b3 e6 2. 0-0-0 Qa3#
  46) NBRKBQRN
  47) NBRKNQBR
  48) NBRKRQBN
  

Solvers

• Reiner Martin (01/09/17 08:35 AM IDT)
• Steven Langerwerf (03/09/17 03:33 PM IDT)
• David Greer (04/09/17 12:39 AM IDT)
• Greg Janée (04/09/17 05:14 PM IDT)
• Robert Gerbicz (04/09/17 08:58 PM IDT)
• Gary M. Gerken (05/09/17 03:00 AM IDT)
• Tyler Mullen (05/09/17 04:48 AM IDT)
• Rickard Björklund (07/09/17 12:56 PM IDT)
• Graham Hemsley (07/09/17 02:41 PM IDT)
• Tamás Haba (07/09/17 09:49 PM IDT)
• Shirish Chinchalkar (09/09/17 04:01 PM IDT)
• Brian Kim (11/09/17 05:04 AM IDT)
• Kandala Srinivas (11/09/17 07:49 PM IDT)
• Alper Halbutogullari (13/09/17 06:16 AM IDT)
• Chris Shannon (15/09/17 09:58 AM IDT)
• Dieter Beckerle (16/09/17 10:17 AM IDT)
• Serge Gautier (18/09/17 12:57 PM IDT)
• Peter Kwang Yeon Kim (18/09/17 09:22 PM IDT)
• Jiwon Park (19/09/17 03:08 AM IDT)
• Leonid Kalmankin (20/09/17 08:45 AM IDT)
• JJ Rabeyrin (22/09/17 11:39 PM IDT)
• Alex Fleischer (23/09/17 03:42 PM IDT)
• Irene Seung Jin Choi (24/09/17 08:08 PM IDT)
• Joehyun Kim (26/09/17 05:51 AM IDT)
• Daniëlle van den Berg (26/09/17 01:03 PM IDT)
• Frank Vernaillen (27/09/17 04:16 PM IDT)
• Tom Harley (27/09/17 07:19 PM IDT)
• Erik Wünstel (30/09/17 03:17 PM IDT)
• Motty Porat (30/09/17 04:47 PM IDT)
• Celine Lee (30/09/17 06:40 PM IDT)
• Jang Hun Choi (30/09/17 08:14 PM IDT)
• Liubing Yu (30/09/17 11:40 PM IDT)