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52 votes
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How is this position possible in a normal game of chess?

Double check is only possible by using discovered check. So either the rook check or the bishop check was discovered by moving something in between on the previous move. I don't see how that's ...
RemcoGerlich's user avatar
  • 28.3k
48 votes
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A mysterious mate in one

Looking at the problem as if the black King is currently invisible...
Jesper Nielsen's user avatar
41 votes
Accepted

Is the position in this trick question reachable?

Even though the board is upside down, the position is still easily legal. [FEN ""] [startply "86"] [StartFlipped "1"] 1. a4 h5 2. g4 h4 3. Bg2 Rh5 4. gxh5 h3 5. h6 e5 6. ...
Rewan Demontay's user avatar
33 votes

Are there any illegal positions that are difficult to spot?

Yes - the less a position looks like a real chess game, the harder it is to spot if it is illegal or not. Sometimes, retrograde analysis is needed to prove a position can be reached in a legal way. ...
Glorfindel's user avatar
  • 24.9k
31 votes
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Given a legal chess position, is there an algorithm that generates a series of moves that lead to it?

The task you are considered is usually called a proof game, named such because the task is to prove that the position is legal. As a genre of puzzles, there are various aesthetic constraints, most ...
A. Rex's user avatar
  • 780
27 votes

Can a unique position be deduced if pieces are replaced by checkers (can see piece color but not type)

Maximum: [FEN "PppppppP/pppppppp/8/8/8/8/PPPPPPPP/pPPPPPPp w KQkq - 0 1"] The board must be right side up because the armies cannot switch sides without some capturing. Given this, all the ...
Noam D. Elkies's user avatar
22 votes
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Least number of moves to achieve a complete switchover of nonpawns in starting setup

As @chakerian's calculations show, 40 moves is the minimum. After a bit of puzzling, I found the solution. [FEN ""] 1. a4 {First, we need to get the rooks in position. They'll be hard to ...
Glorfindel's user avatar
  • 24.9k
21 votes
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Prove that White is not allowed to castle here

This is actually a rather typical retrograde problem, just start with the most basic observations: We see that black is missing both rooks and the f8 bishop. Given black's pawn structure it's easy to ...
Ellie's user avatar
  • 12k
19 votes
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Identify a problem where a potentially winning move draws because of the 50 move rule

There are dozens of problems that illustrate a potential winning moves that instead leads to a draw because of the 50 move rule. One example is the following mate in four published by Léon Loewenton ...
Étienne's user avatar
  • 813
18 votes

Are there any illegal positions that are difficult to spot?

If we define "illegal position" as a position that cannot happen in a game using legal moves, I think that the most difficult to spot would be positions that look normal, but are impossible to achieve....
Alex Petrov's user avatar
  • 1,238
18 votes

How to solve proof games?

Although solving proofgames is not that difficult, the large number of moves involved may seem impressive at first. Let me share you a few tips by showing how I solve a proofgame. [Title "Étienne ...
Étienne's user avatar
  • 813
16 votes
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Could a chess engine do retro analysis?

Engines like Stockfish and Komodo are not able to work out the previous moves, because that is not what they are programmed for. However, it is vanishingly unlikely that anybody can ever program an ...
Remellion's user avatar
  • 5,040
15 votes

A mysterious mate in one

A solution may be that it used to be possible to Would that really explain Perhaps, in the sense that
Glorfindel's user avatar
  • 24.9k
14 votes
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Can white win in this almost 20 year old puzzle?

The solution is This works because
Glorfindel's user avatar
  • 24.9k
12 votes
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"Knight rebus"-Decipher an encoded chess position

Assume the board is in it's usual position (the bottom row is the first row) then this is the solution: [FEN "1B6/8/1k6/R7/1n6/2K5/r6p/q1r1n3 - - - 0 1"] and Black's last move was b2xc1R++. I could ...
Glorfindel's user avatar
  • 24.9k
12 votes

What was Black's last move?

There is only one black piece left, so the last move was with the king. Black's last move was obviously Kg1-h2. The king could not have come from h3, because there is no way the white pawn could have ...
user1583209's user avatar
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12 votes
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Can you mate with each of your 16 pieces on its original square?

Obviously the last white move was 16. Nf3g1+. I note that black needs at least 15 moves to place the pieces as they are: 4 moves to swap queen with rook as they are (various movements possible), 2 ...
user1583209's user avatar
  • 20.8k
12 votes

Which methods can be used to prove that a position is illegal?

Easy illegality is easy: not exactly 1 king on both sides, both kings in check, pawns on the final ranks. It's also fairly easy to tally promoted material and subtract the missing pawns. A quick ...
Hauke Reddmann's user avatar
11 votes
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Can we say for sure that Black's king has not moved?

The conditions you gave are incomplete. The conditions include that black (to move) can castle; it's hidden in Smullyan's original problem text. From the English book, last paragraph of the problem ...
Remellion's user avatar
  • 5,040
10 votes

Least number of moves to achieve a complete switchover of nonpawns in starting setup

Shouldn't the minimum be 40?. I don't have any result to show yet but it seems that: Pawns (black and white): 8 moves Rooks (black and white): 10 moves Kings (black and white): 7 moves Queens (...
chackerian's user avatar
10 votes

Which chess position requires the most moves to reach?

This was published about in the latest entry of Tim Krabbé's Chess Diary. Harry Goldsteen has put some research into this and came up with a position which is reachable only in 185 moves: [FEN ""] [...
Glorfindel's user avatar
  • 24.9k
10 votes

Given a legal chess position, is there an algorithm that generates a series of moves that lead to it?

If you are familiar with mathematical induction then it should be clear to you that the answer is trivially "Yes". Just as for any position (legal or otherwise) it is possible to use the ...
Brian Towers's user avatar
  • 99.3k
10 votes
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Do any unique proof games feature an en-passant capture?

There are plenty! There are currently 158 currently in the Die Schwalbe Chess Problem Database. For example, here is one with three consecutive en passants! [Title "Thierry Le Gleuher, R028c ...
Rewan Demontay's user avatar
9 votes

Prove that White is not allowed to castle here

This problem is by Raymond Smullyan, and is from his The Chess Mysteries of Sherlock Holmes (p.54 of the Hutchinson edition). Phonon's analysis is mostly sound, except that we don't know which black ...
Rosie F's user avatar
  • 6,485
9 votes

Can you mate with each of your 16 pieces on its original square?

The thoughts mentioned in user1583209's answer more or less summed up mine, but I couldn't find a way to get the king out in time without requiring extra moves. The final trick is [FEN ""] 1. Nc3 h5 ...
Glorfindel's user avatar
  • 24.9k
9 votes
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Seeking a particular problem

I found a problem that perfectly fits your description! I’ve played the position back a move for the double step. [Title "Kurt Keller, Stuttgarter Nachrichten & Südwest Presse (Ulm) 1993, ...
Rewan Demontay's user avatar
9 votes

From Mate-in-3 to Mate-in-1

Spotting potential mates isn't too difficult. There are a couple of obvious ones involving the b and h pawns which aren't far off from promoting. An immediate b7 threatens b8=N# for example. It can ...
Brian Towers's user avatar
  • 99.3k
9 votes

Do you know this proof game?

The reasoning is as follows: So the time series of key events:
MikeD's user avatar
  • 1,994
9 votes
Accepted

Legal positions with one color to move only?

You found most of the possibilities where an argument about parity can determine which side has the move (however, this is not all the 32-pieces positions, see the edit at the bottom), which all have ...
Evargalo's user avatar
  • 16.5k
9 votes
Accepted

What are "monochromatic" retrograde analysis problems?

"Monochromatic" (or "monochrome") is a popular fairy condition with nearly 450 examples in the PDB database: https://pdb.dieschwalbe.de/overview.jsp?expression=K%3D%27Monochromatic%...
Laska's user avatar
  • 13.1k

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