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Often, a puzzle type of problem in which a tactical or positional solution is required, like White/Black to move and win”, in what is often a middlegame or endgame-esqe position. But a puzzle can also be a chess riddle, chess math, or any other non-normal chess problem. Questions about solving puzzles, puzzle apps and websites, how to understand the idea behind a puzzle, etc. are also on-topic.

6 votes
Accepted

I'm not quite sure I understand this daily puzzle on Lichess (9/6/24)

Seems Black should just play 19. ... Qxf4; White can't recapture because the Re6 pins the White e-pawn. White will reply 20. Bxe6, grabbing a Rook while also putting the bQf4 en prise. But Black reto …
Noam D. Elkies's user avatar
9 votes
Accepted

Threefold repetition: what's the minimum number of pieces and/or material points required?

4 pieces is the minimum, and is attained by this position though Black has the option of trading Q for N to a bare-king draw: [Title "Draw by perpetual check or insufficient material"] [FEN "8/8/8/8/8 …
Noam D. Elkies's user avatar
21 votes
Accepted

What's the maximum amount of material that a puzzle with unique solution can have?

This must be the maximum for an illegal position (adapted from David's attempt): [Title "_David_, v. NDE: White to move and win"] [FEN "qqqqqqqq/qkqQqqqq/qqqQqqqq/qQQQqqqq/qqqqQqqq/qqqqqqqq/qqqqqqQQ/q …
Noam D. Elkies's user avatar
0 votes
Accepted

Relationship between having a selfmate and having a checkmate?

There are certainly exceptions. Most easily, when the opponent has only the King left, there's usually a forced checkmate but there cannot be a selfmate. Likewise with Q vs. N and Q vs. B. In fact …
Noam D. Elkies's user avatar
11 votes

Most mate options after 6 moves

11 without discovered checks: [FEN ""] [startply "12"] 1. e3 e6 2. d4 Ke7 3. Bc4 Kf6 4. Nh3 Kf5 5. Bxe6+ Ke4 6. Qh5 Qe8
Noam D. Elkies's user avatar
8 votes

Most mate options after 6 moves

5.5 moves to 14 fool's mates: [FEN ""] [startply "11"] 1. b4 e6 2. Bb2 Qh4 3. Bxg7 Ne7 4. Bb2 Rg8 5. g3 Rxg3 6. f4 For 6.0 moves, start with something like 1. a3 and then reverse the colors (1. a3 b …
Noam D. Elkies's user avatar
3 votes

Max percentage of mating pieces

It's easy to get 16/17 = 94.1% [FEN "4B3/4Q3/3QQQ2/1N2B2N/4k3/1Q5Q/3PKP2/2R1Q1R1 w - - 0 1"] On further thought that's not legal for lack of a previous Black move. This should be fixable, but meanwhi …
Noam D. Elkies's user avatar
1 vote

Why is this puzzle solved

It's won for White because Q+R coordinate to attack the exposed bK which Black can't defend for long. I assume you started 1 Rg3 g5 2 Rxg5+ Kf7 3 Rxf6+. Then Kxf6 4 Rg6+ and now: 4 ... Ke7 5 Qg7+ Rf7 …
Noam D. Elkies's user avatar
6 votes

Why do chess puzzles need a unique solution?

Basically for the same reason that we're not impressed by a win by queen sacrifice if there was also a pedestrian one- or two-move mate. There are chess problems that deliberately have more than one s …
Noam D. Elkies's user avatar
9 votes
Accepted

Trying to remember a zugzwang puzzle/study position

The original position has the White King on a4, no White pawn. It's the end of a composed study by Gorgiev that I find as #753 in Sutherland and Lommer's 1234 Modern End-Game Studies (1938, Dover rep …
Noam D. Elkies's user avatar
11 votes

Chess positions that are easy for humans but near impossible or confusing for computers

One way to fool some computers is to give them a fortress and then offer material to trick them into opening the portcullis. For example: [Title "White to draw"] [FEN "8/8/pr1k4/Pp2rp1p/1Pp1pPpP/2PpP …
Noam D. Elkies's user avatar
6 votes
Accepted

How many different knight's tours are there?

Wikipedia quotes several sources for a count of 26,534,728,821,064 for the number of closed directed tours of the 8x8 board. As Brian Towers notes in his answer, that is equivalent to the count of Kn …
Noam D. Elkies's user avatar