September 2017 - Challenge

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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:
  1. The bishops must occupy squares of opposite colors.
  2. The king must occupy a square between the two rooks.
    3. 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?

Update (4/9): Update 4/9: Pay attention to the special Castling rules, see also at the Wikipedia link: https://en.wikipedia.org/wiki/Chess960

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 30/08/2017 @ 12:00 PM EST
Solution: 02/10/2017 @ 12:00 PM EST
List Updated: 28/09/2017 @ 12:00 PM EST

People who answered correctly:

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)