# [Retros] Shortest checkmates in shortest proof games

fieberg at gcr.com fieberg at gcr.com
Fri Oct 4 05:33:17 EDT 2002

Hello Noam,
thanks for the nice improvements!

Considering the promotions the original intention was that the piece itself
checkmates.

However, the task could be extended to:
- Promote the pawn and checkmate with the promoted piece!

This extension would require 8 (pawns) x 4 (promotions) = 32 further SPGs
(in addition to the 16 SPGs) of which 4 are composed by you (a2-Q, c2-Q,
f2-Q, h2-Q).

Best regards,
Christoph

Current record table is:

Pawns: a2(5,5-CF), b2(4,5-CF), c2(5,5-CF), d2(4,5-CF), e2(4,5-CF),
f2(5,5-CF), g2(4,5-CF), h2(5,5-CF)
Knights: b1(4,5-CF), g1(4,5-NE)
Bishops: c1(4,5-CF), f1(3,5-CF)
Rooks: a1(4,5-NE), h1(4,5-CF)
Queen: d1(2,5-CF)
King: e1(5,5-CF) [King checkmates by discovered attack]

Promoted pawns (Q): a2(4,5-NE), c2(4,5-NE), f2(4,5-NE), h2(4,5-NE)
Promoted pawns (R):
Promoted Pawns (B):
Promoted Pawns (N):

CF = Christoph Fieberg
NE = Noam D. Elkies

I assume that the SPG in 2,5 moves with white Qd1 checkmating is the sole
SPG in 2,5 moves fullfilling the task.
Which other of the 16 + 32 SPGs are *sole* ones?
I consider e.g. the SPG with white Ke1 as a good candidate.

----- Forwarded by Christoph Fieberg/GCR-Germany/GRN on 04.10.02 11:09
-----

Noam Elkies
<elkies at math.harv To: Retros at janko.at
ard.edu> cc:
Sent by: Subject: Re: [Retros] Shortest checkmates in shortest proof games
o.at

04.10.02 07:25
retros

Interesting task; it rings a bell but I cannot recall an exact
anticipation. Two improvements:

> 9) White checkmates with Rook a1: SPG in 5,5 moves

4.5 moves: 1 a4 b5 2 ab c5 3 R:a7 Qb6 4 Rc7 Qd6 5 R:c8#
(similar to your Rh1 SPG; C+ Popeye 3.41 in 0.04 second)

> 15) White checkmates with Knight g1: SPG in 5,5 moves

4.5 moves: 1 Nf3 g5 2 Ne5 g4 3 N:d7 e5 4 a3 Ne7 5 Nf6#
(C+ Popeye 3.41 in 0.04 second)

Perhaps some more improvements:

> 3) White checkmates with Pawn c2: SPG in 5,5 moves

Again only 4.5 -- if 1 c4 e6 2 c5 Bd6 3 c:d6 Kf8 4 dc d6 5 c:d8=Q#
(C+ Popeye 3.41 in 0.02 second) is allowed... Likewise the 5.5 moves
for a2,c2,h2 can be reduced to 4.5 with a promotion mate:

1 a4 c6 2 a5 Qc7 3 a6 Qf4 4 ab d6 5 b:c8=Q# (C+ in 0.01 sec.)
1 f4 e5 2 fe Bd6 3 e:d6 Kf8 4 dc d6 5 c:d8=Q# (C+ in 0.02 sec.)
1 h4 c6 2 h5 Qc7 3 h6 Kd8 4 hg h6 5 g:f8=Q# (C+ in 0.02 sec.)

--Noam D. Elkies

----- Forwarded by Christoph Fieberg/GCR-Germany/GRN on 04.10.02 11:16
-----

fieberg at gcr.com
Sent by: To: Retros at janko.at
o.at Subject: [Retros] Shortest checkmates in shortest proof games

04.10.02 02:51
retros

Yesterday I asked myself what the shortest number of moves might be for
composing checkmates in a shortest proof game. I found some short
checkmates but then I wanted SPGs for every white piece checkmating.
Therefore I composed 16 SPGs and the maximum number of moves I needed was
5,5 (for the difficult a, c, f and h-pawns, the king, the night g1 and the
rook a1)

Here are my records for every white checkmating piece (number of moves in
brackets).
Pawns: a(5,5), b(4,5), c(5,5), d(4,5), e(4,5), f(5,5), g(4,5), h(5,5)
Knights: b(4,5)*, g(5,5)*
Bishops: c(4,5), f(3,5)*
Rooks: a(5,5)*, h(4,5)*
Queen: d(2,5)*
King: e(5,5) ? King mates by discovered attack

*White moves only pawns and the checkmating piece!

You can find the solutions below after the asterisks (don't check up too
early).
All solutions are computerproofed.

Open questions:
1. Are shorter SPGs for the white checkmating pieces possible?
2. Which of the SPGs are unique in the sense that no alternative SPG can be
composed with the same minimum amount of moves?
3. What are the shortest 16 SPGs for every black checkmating piece?

Have fun,
Christoph Fieberg
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Solutions:

1) White checkmates with Pawn a2:
SPG in 5,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq1bnr/ppp1pppp/Q2p4/8/1k6/P2PB3/1PP1PPPP/RN2KBNR b KQ - 0 6
1.d3 d6 2.Qd2 Kd7 3.Qa5 Kc6 4.Qa6+ Kc5 5.Be3+ Kb4 6.a3#

2) White checkmates with Pawn b2:
SPG in 4,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnb2bnr/pppqpppp/2kp4/1P6/3B4/2N5/P1PPPPPP/R2QKBNR b KQ - 0 5
1.b4 d6 2.Bb2 Kd7 3.Bd4 Kc6 4.Nc3 Qd7 5.b5#

3) White checkmates with Pawn c2:
SPG in 5,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq1bnr/ppp1pppp/3p4/3R4/Pk6/N1P5/1P1PPPPP/2BQKBNR b K - 0 6
1.a4 d6 2.Ra3 Kd7 3.Rd3 Kc6 4.Na3 Kc5 5.Rd5+ Kb4 6.c3#

4) White checkmates with Pawn d2:
SPG in 4,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnb2bnr/pppqpppp/2kp4/Q2P4/8/2P5/PP2PPPP/RNB1KBNR b KQ - 0 5
1.d4 d6 2.Qd2 Kd7 3.Qa5 Kc6 4.c3 Qd7 5.d5#

5) White checkmates with Pawn e2:
SPG in 4,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq1b1r/ppppnppp/4pk2/4P2Q/8/5N2/PPPP1PPP/RNB1KBR1 b Q - 0 5
1.e4 e6 2.Qh5 Ke7 3.Nf3 Kf6 4.Rg1 Ne7 5.e5#

6) White checkmates with Pawn f2:
SPG in 5,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq1b1r/ppp1pppp/3p1n2/4k3/4PP2/1Q1P4/PPP1N1PP/RNB1KB1R b KQ f3 0 6
1.e4 d6 2.Qf3 Kd7 3.Ne2 Ke6 4.Qb3+ Ke5 5.d3 Nf6 6.f4#

7) White checkmates with Pawn g2:
SPG in 4,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq2nr/ppppbppp/4pk2/6P1/4B3/5N2/PPPPPP1P/RNBQK2R b KQ - 0 5
1.g4 e6 2.Bg2 Ke7 3.Be4 Kf6 4.Nf3 Le7 5.g5#

8) White checkmates with Pawn h2:
SPG in 5,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq1bnr/pppp1ppQ/4p3/4P3/6k1/3P3P/PPP2PP1/RNB1KBNR b KQ - 0 6
1.e4 e6 2.Qh5 Ke7 3.Qxh7 Kf6 4.e5+ Kg5 5.d3+ Kg4 6.h3#

9) White checkmates with Rook a1:
SPG in 5,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbqk1R1/pppppp2/8/6p1/P7/8/1bPPPPPP/1N1QKBNR b Kq - 0 6
1.a4 g5 2.Ra3 Bg7 3.Rh3 Bxb2 4.Rxh7 Bxc1 5.Rxh8 Lb2 6.Rxg8#

10) White checkmates with Knight b1:
SPG in 4,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
1r1qkb1r/pp1pnppp/2nN4/2p5/8/8/PPPPPPPP/R1BQKBNR b KQk - 0 5
1.Nc3 c5 2.Nd5 Nc6 3.Nxe7 Rb8 4.Nxc8 Nge7 5.Nd6#

11) White checkmates with Bishop c1:
SPG in 4,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq1bnr/ppp1pppp/3p4/2kP4/8/1Q2B3/PPP1PPPP/RN2KBNR b KQ - 0 5
1.d4.d6 2.Qd3 Kd7 3.Qb3 Kc6 4.d5+ Kc5 5.Be3#

12) White checkmates with Queen d1:
SPG in 2,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbqkbnr/ppppp2p/8/5PpQ/8/8/PPPP1PPP/RNB1KBNR b KQkq - 0 3
1.e4 f5 2.exf5 g5 3.Qh5#

13) White checkmates with King e1 (by discovered attack):
SPG in 5,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbq1bnr/ppppp2p/5pp1/6k1/3PK3/7Q/PPP1PPPP/RNB2BNR b - - 0 6
1.d4 f6 2.Qd3 Kf7 3.Qh3 Kg6 4.Kd2 Kg5 5.Ke3 g6 6.Ke4#

14) White checkmates with Bishop f1:
SPG in 3,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbqkbnr/ppppp1p1/6Bp/8/8/4P3/PPPP1PPP/RNBQK1NR b KQkq - 0 4
1.e3 f6 2.Bd3 f5 3.Bxf5 h6 4.Bg6#!!

15) White checkmates with Knight g1:
SPG in 5,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
r2qkb1r/ppnpnppp/3N4/8/8/8/PPPPPPPP/RNBQKB1R b KQkq - 0 6
1.Nf3 e5 2.Nxe5 c6 3.Nxc6 Na6 4.Ne7 Nc7 5.Nxc8 Ne7 6.Nd6#

16) White checkmates with Rook h1:
SPG in 4,5 moves - Christoph Fieberg; Retros mailing list 4.10.2002
rnbqk1R1/pppppp2/8/6P1/8/8/P1PPPPP1/RNbQKBN1 b Qq - 0 5
1.h4 g5 2.hxg5 Bg7 3.Rxh7 Bxb2 4.Rxh8 Bxc1 5.Rxg8#