Every Wednesday in my town, there's a pub quiz at the Queens Head. Richard, the landlord, runs a very quirky quiz where the prize hardly ever goes to the best team. A typical announcement would be, "Totally chosen at random by a passing Nun, tonight's Star Prize is a Luxury Deluxe bottle of Prosecco, going to the team that comes third!".
He also takes out adverts for the pub in a local monthly magazine called The Fuddler. Every month, along with the advert, there's a mate-in-2 chess puzzle. Richard is a chess fan; I don't know where he gets the puzzles from, but they're always quite fiendish.
In the advert puzzle shown (5), the Black King is hemmed in and can't move. All White needs to do is give check, which looks easy: RxN, which also removes the troublesome Knight, and the King still has nowhere to go. But there's an escape: Qf5, blocking the Rook check. The Rook can simply take the Queen, giving check again, but now Black has another escape move: Ke4, since the Bishop is now blocked by the Rook.
And that's as far as I got with this one.
This happens a lot. Even if I think I've worked out the answer, I'm never completely sure I haven't missed something. And, slightly annoyingly, there's never any answer to the puzzle in the next issue. But I'd like to know what I've missed, mainly to get that Aha! moment. So… I decided to find some tools to help.
The first thing I looked at was Lichess, which is a great free online chess tool, and accepts board positions in FEN format. For the puzzle above, the FEN format is:
5K2/3PRnQB/2p5/3p4/5k2/7q/2N5/4N3 w - - 0 1
You can get it to set up the position like this. If you turn on Stockfish analysis mode, it will will come up with a mate in 2:
1. Ne3
2. Qf5 N3g2#
Hmm. OK, that's mate, but what if Black had done something different? I couldn't figure out how to get any alternative Black moves; maybe I was missing something. Lichess has an API, but it doesn't seem to have anything to help solve chess puzzles.
Looking around some more, I found another option: Popeye. Not the sailor, but a standalone program specifically for solving chess puzzles. After installing it, and reading just enough of the arcane manual to figure out how to encode the puzzle, I cobbled together this input:
Begin
Origin Fuddler, November 2022
Pieces White Se1 Sc2 Pd7 Re7 Qg7 Bh7 Kf8
Black Qh3 Kf4 Pd5 Pc6 Sf7
Option NoBoard Variation
Stipulation #2
End
Instead of FEN notation, it lists the Black and White pieces individually
by position. Strangely, Popeye uses S to indicate a Knight instead of
N.1 It's the Variation option which gets all the possible Black
replies; without that, you just get the winning first move.
Feeding it into Popeye, this is what comes out:
1.Sc2-e3 ! zugzwang.
1...Qh3-f1
2.Qg7-g4 #
1...Qh3-g2
2.Se3*g2 #
1...Qh3*d7
2.Se3-g2 #
1...Qh3-e6
2.Se3-g2 #
1...Qh3-f5
2.Se3-g2 #
1...Qh3-g4
2.Qg7*g4 #
1...Qh3-h1
2.Qg7-g4 #
1...Qh3-h2
2.Qg7-g4 #
1...Qh3*e3
2.Re7*f7 #
1...Qh3-f3
2.Se1-d3 #
1...Qh3-g3
2.Qg7-f6 #
1...Qh3*h7
2.Qg7-g4 #
1...Qh3-h6
2.Se3-g2 #
1...Qh3-h5
2.Se3-g2 #
1...Qh3-h4
2.Se3-g2 #
1...d5-d4
2.Re7-e4 #
1...c6-c5
2.Se3*d5 #
1...Sf7-d6
2.Qg7-e5 #
1...Sf7-e5
2.Qg7*e5 #
1...Sf7-g5
2.Qg7-e5 #
1...Sf7-h6
2.Qg7-e5 #
1...Sf7-h8
2.Qg7-e5 #
1...Sf7-d8
2.Qg7-e5 #
So the winning move is Nc2-e3, which agrees with Lichess. But now it's a bit clearer why: It leaves Black in a Zugzwang position such that any of 23 possible moves has a mating reply. It's safe to say I would not have worked that out.
Well, Popeye did what I asked it, but I still wasn't happy with the method. The Popeye input syntax is quite verbose; I much prefer the FEN format used by Lichess. And I think the output could be summarized more succinctly, by grouping the moves by mating reply. Could I do better?
I didn't find any other tools specifically for the mate-in-2 problem. But I did find a Python chess module. Its documentation says it can manipulate chess boards and positions in various ways, make moves, detect checkmate, and a bunch of other things. Sounds good! Let's have a go with it.
First, let's see if we can get it to read my puzzle FEN position.
fen = "5K2/3PRnQB/2p5/3p4/5k2/7q/2N5/4N3"
board = chess.Board(fen)
print(board)
Running this, we get:
. . . . . K . .
. . . P R n Q B
. . p . . . . .
. . . p . . . .
. . . . . k . .
. . . . . . . q
. . N . . . . .
. . . . N . . .
Cute. An ASCII board showing the position. Digging into the docs a bit more, it turns out that it can also write SVG files:
from pathlib import Path
from chess import svg
def print_svg(board, filename):
Path(filename).write_text(svg.board(board))
print_svg(board, "fuddler.svg")
Here's what the resulting file looks like:
Much nicer!
Looking further at the docs, there's a Board property that looks very
useful: legal_moves. It yields all the legal moves from that board
position as Move objects. There are also push() and pop() methods to
perform (and undo) moves on a board, modifying it in-place. And finally,
there's an is_checkmate() method to see if the side to move on the
Board is in checkmate. This is looking promising!
The first thing to do is to make a way to iterate over the move tree which
(a) returns the move in a human-readable format, and (b) undoes the move
when analysis of that part of the tree is done. Here's my attempt: the
make_legal_move() iterator. For each legal move it updates the board,
yields the move in SAN format, and undoes the move afterwards.
def make_legal_move(board):
for move in board.legal_moves:
try:
san = board.san(move)
board.push(move)
yield san
finally:
board.pop()
Let's see if that works for the puzzle board. It should produce a list of valid first moves for White.
import textwrap
moves = ", ".join(make_legal_move(board))
print(textwrap.fill(moves))
And here's the result:
Kg8, Ke8, Kxf7, Bg8, Bg6, Bf5, Be4, Bd3, Qh8, Qg8, Qxf7+, Qh6+, Qg6,
Qf6+, Qg5+, Qe5+, Qg4+, Qd4+, Qg3+, Qc3, Qg2, Qb2, Qg1, Qa1, Re8,
Rxf7+, Re6, Re5, Re4+, Re3, Re2, Nd4, Nb4, Ne3, Na3, Na1, Nf3, Nd3+,
Ng2+, d8=Q, d8=R, d8=B, d8=N
Wow, quite a lot of options! Checking against the board, it does look like these are all White's valid moves.
OK, the next problem is how to use this function to look ahead and find a mate-in-2 solution to the puzzle. After a few iterations and dead ends, here's what I came up with:
def mate_in_2(board):
# Look at all first moves for white.
for move in make_legal_move(board):
# Keep track of Black's replies, and White's mating moves.
replies = {}
# Does Black have a move that avoids mate?
avoidmate = False
# Check Black's replies.
for reply in make_legal_move(board):
# Is there a mating move from this position?
canmate = False
for mating_move in make_legal_move(board):
if board.is_checkmate():
replies[reply] = mating_move
canmate = True
break
# If not, Black can escape.
if not canmate:
avoidmate = True
break
# If black can't avoid mate, it's a solution.
if not avoidmate:
yield move, replies
It takes a FEN position, and for each solution, yields a 2-tuple: the
winning move for White, and a dict of possible Black replies, each reply
mapped to the final mating move. Let's use this to print out the solution
in a chess-style format:
board = chess.Board(fen)
for move, replies in mate_in_2(board):
print(f"1. {move}")
for reply, mating_move in sorted(replies.items()):
print(f"1. ... {reply:6} 2. {mating_move}")
Running this, we get:
1. Ne3
1. ... Nd6 2. Qe5#
1. ... Nd8 2. Qe5#
1. ... Ne5 2. Qxe5#
1. ... Ng5 2. Qe5#
1. ... Nh6 2. Qe5#
1. ... Nh8 2. Qe5#
1. ... Qe6 2. N3g2#
1. ... Qf1 2. Qg4#
1. ... Qf3 2. Nd3#
1. ... Qf5 2. N3g2#
1. ... Qg2 2. N3xg2#
1. ... Qg3 2. Qf6#
1. ... Qg4 2. Qxg4#
1. ... Qh1 2. Qg4#
1. ... Qh2 2. Qg4#
1. ... Qh4 2. N3g2#
1. ... Qh5 2. N3g2#
1. ... Qh6 2. N3g2#
1. ... Qxd7 2. N3g2#
1. ... Qxe3 2. Rxf7#
1. ... Qxh7 2. Qg4#
1. ... c5 2. Nxd5#
1. ... d4 2. Re4#
Hey, that's pretty nice, and it agrees with the Popeye output (apart from
ordering). But I still think it would be nicer to group all the replies by
mating move. Here's a function to do that on the replies returned by the
mate_in_2 function, and prettyprint them:
def print_solution(move, replies, separator=" "):
print(f"1. {move}")
# Group replies by mating move.
mating_moves = defaultdict(list)
for reply, mating_move in replies.items():
mating_moves[mating_move].append(reply)
# Build output lines.
outputs = []
for mating_move, replies in mating_moves.items():
replytext = separator.join(replies)
outputs.append([replytext, mating_move])
# Print them.
maxlen = max(len(text) for (text, move) in outputs)
for replytext, mating_move in outputs:
print("1. ... %-*s 2. %s" % (maxlen, replytext, mating_move))
Let's use this to print the example solution:
1. Ne3
1. ... Nh8 Nd8 Nh6 Nd6 Ng5 2. Qe5#
1. ... Ne5 2. Qxe5#
1. ... Qxh7 Qh2 Qh1 Qf1 2. Qg4#
1. ... Qxd7 Qh6 Qe6 Qh5 Qf5 Qh4 2. N3g2#
1. ... Qg4 2. Qxg4#
1. ... Qg3 2. Qf6#
1. ... Qf3 2. Nd3#
1. ... Qxe3 2. Rxf7#
1. ... Qg2 2. N3xg2#
1. ... c5 2. Nxd5#
1. ... d4 2. Re4#
And finally (for now, at least) I'm content.
Copyright (c) 2022, Glenn Hutchings <zondo42@gmail.com>
All rights reserved.
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0
International License. To view a copy of this license, visit
http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative
Commons, PO Box 1866, Mountain View, CA 94042, USA.
1 At first I thought this was a quirk of Popeye, but no, it's a standard thing: the S is from the German for Knight, Springer.