Die Schwalbe

3 problem(s) found in 3531 milliseconds (displaying 3 problem(s)). [COMMENTDATE>=20200919 AND NOT K='Hilfsrückzüger' AND G='Mathematics']

1 - P1182074
William A. Shinkman
666 The Golden Argosy , p. 286, 1929
P1182074
(5+5)
Pattaufhebung, wodurch Schwarz 32 Züge erhält
1. Lb4
play all play one stop play next play all
Romantischer Rekord
A.Buchanan: This kind of problem is traditionally in PDB placed in the mathematics genre, rather than fairy, because it involves, you know, counting stuff (2020-11-22)
comment
Keywords: Construction record
Genre: Mathematics
FEN: 8/8/7K/p7/R3b2k/6rP/4p3/4B1N1
Input: HBae, 2010-12-09
Last update: A.Buchanan, 2020-11-22 more...
2 - P1249837
George Burt Spencer
St. Paul Dispatch 1906
P1249837
(34+15) C+
#2 auf jeder Reihe und jeder Linie
a) 1. Lc2! ... 2. Ld3# 1. ... Kxa1 Lc1#
b) 1. Dd4! ... 2. Dxb4#
c) 1. Dxc6! ... 2. Dxc5#
d) 1. Txd4 ... 2. Txd5 1. ... Kc5 2. Db4# 1. ... Ke5 2. Df4#
e) 1. De4! ... 2. Db1#,Dh1# 1. ... Kd1 2. Db1# 1. ... Kf1 2. Dh1# (Fleck)
f) 1. Ld5+! Ke8 2. Dc8#
g) 1. Dd7! Kf8 2. Df7# 1. ... Kh8 2. Dh7#
h) 1. De4! ... 2. Dg4#
i) 1. Ld4! ... 2. Sg3#
j) 1. Db4! Ka1 2. Da3#,Db1# (dual)
k) 1. Lgd6! Kc2 2. Ld1# 1. ... Kc4 2. Ld5#
l) 1. Dc8+! Kd3 2. Dc2# 1. ... Kd5 2. Dc6#
m) 1. Ta3! ... 2. Th3#
n) 1. Kb7! ... 2. Dxc6#
o) 1. De5! ... 2. Dg7#
p) 1. Tc7! Kh8 2. Dxf8#
play all play one stop play next play all

Duplicate Diagram: P1126102, P1129822, P1145270, P1145376, P1149794, P1159233, P1164692, P1164885, P1175321

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comment
Keywords: Oneliner (16)
Genre: 2#, Mathematics
Computer test: Popeye Windows-64Bit v4.69
FEN: 2RKQbk1/2QB1k1K/KQpk1BPN/RKpp1QPk/Bpkp1KQn/BkNRKBBN/k1BQP1K1/BBK1kN1Q
Input: Nikolai Beluhov, 2012-09-24
Last update: A.Buchanan, 2020-11-27 more...
3 - P1312478
Nenad Petrovic
Problem 7, p. 109, 03/1952
P1312478
(9+4)
#2
Projective Chess
Solution:
1. Kg1!
1. ... Ke4,Kf3 2. D-PH#
1. ... d2,Kg4,Kg5 2. D-PD1#
1. ... Sc7~ 2. D-PV#
1. ... Sb6~ 2. D-PD2#

Non-solutions
1. D-PD2? Sc7a8,Sc7d5!
1. D-PH+? Kg5!
1. D-PD1+? Ke4!
1. Kh1,Kg2? Sb6a8,Sb6d5!
1. Kh3? Kf3!
1. h6? Kg5!
1. a3,a4,a7,d6,f6? Sb6~!
1. Dxb6,Dxc7,Dc6,Df2,Dg1,Db4,Da3? Ke5!
1. De5? Kxe5!
1. De3? Kxe3!
1. Dd4+ Kf3!
1. Db5,Dd5? SxD!
1. Da5? Sc7~! (the reason I think for wBa2a6)
play all play one stop play next play all
In der Lösung bezeichnet 'PH' das projektive Feld in horizontaler Richtung; 'PV' das projektive Feld in vertikaler Richtung; 'PD1' ist das projektive Feld in Richtung der Diagonale a1-h8; 'PD2' ist das projektive Feld in Richtung der Diagonale a8-h1.

A.Buchanan: Together with excellent paradoxical key, and the 4 clean mating lines, a large number of potential cooks are prevented quite economically (see non-solutions, above). wBf6 in particular has many roles. So on this occasion a minor dual at one point later in the solution seems completely acceptable. A very original composition!
Interessanterweise werden in der Lösung alle vier unendlich entfernten Felder des projektiven Schachbretts benutzt.
A.Buchanan: In projective geometry, every family of parallel straight lines intersects at an infinitely distant point. Chess problem composers in the former Yugoslavia have adapted this idea for the chessboard, adding four special squares “at infinity.”

Now a queen on a bare board, for example, can zoom off to the west (or east) and reach a square “at infinity” from which she attacks every rank on the board simultaneously from both directions. She might also zoom to the north (or south) to reach a different square at infinity; from this one she attacks every file simultaneously, again from both directions. Finally she can zoom to the northwest or southeast and attack all the diagonals parallel to a8-h1, or zoom to the northeast or southwest and attack all the diagonals parallel to a1-h8. These four “infinity squares,” plus the regular board, make up the field of play. (2015-11-20)
Henrik Juel: Fine explanation, Andrew, but I still need to see the intended solution (if you know it); this may also clarify the weird stipulation (2015-11-20)
Alfred Pfeiffer: Diese Schachvariante wurde 1952 von Prof. Lav Rajcic und Nenad Petrovic erfunden (D.B.Pritchard: The Encyclopedia of Chess Variants) (2015-11-20)
A.Buchanan: The articulate explanation is not mine: I found it at http://www.futilitycloset.com/?s=chess
I think one needs to add that only line pieces have the privilege to leave the regular board in this way. Which suggests another variant with Nightriders. Now there are another 4 squares accessible only by Nightriders. (2015-11-21)
Henrik Juel: Thanks, Andrew and Alfred
Nice key, but too bad about the trial after 1... Kg3 (2015-11-21)
Henrik Juel: Andrew has pointed out that the flaw after 1... Kg3 is only a dual (2015-11-22)
A.Buchanan: Someone asks me: is there a cook? 1. D-PD2 Sc7a8,Sc7d5 can be answered by 2. Kh3# (2020-11-10)
A.Buchanan: By the way: the squares at infinity are on a straight line, but that cannot be navigated by the queen. For suppose the contrary: then the direction of movement along that line would have to be parallel to some direction of movement of the queen, i.e. by symmetry parallel to *all* directions of movement of a queen, i.e. since lines parallel to one line are parallel to one another, we conclude that all lines on the board are parallel to one another. This is absurd, so the queen cannot navigate the line at infinity (2020-11-10)
comment
Keywords: Projective Chess, no 8x8 board
Genre: Fairies, Mathematics
FEN: 8/2n5/Pn1P1P2/2Q2P1P/2P2k2/3p4/P6K/8
Reprints: Matematika Na Shahmatnoi Doske
Schachmaty i matematika [Gik] , p. 119, 1983
Schach und Mathematik [Gik] , p. 150, 1986
Input: A.Buchanan, 2015-11-20
Last update: A.Buchanan, 2020-11-10 more...
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The problems of this query have been registered by the following contributors:

HBae (1)
Nikolai Beluhov (1)
A.Buchanan (1)