Four chess logic puzzles

Hi, Here are four interesting chess logic puzzles, that I hope you will like. By logic chess puzzles, I mean those that are not commonly known as 'studies', and which need a fairly strong classic chess understanding. These puzzles take as a base the chess board, most of the time the pieces move along as in classic chess, but the rules must not necessarily be the same. I would includ retrograd chess problems in this category. Just for info, if you want a superb book, and not too hard, on retrograd chess problems, I would highly recommend: Chess Mysteries of Sherlock Holmes by Dr. Raymond Smullyan, a true masterpiece I would say !

The first two problems are by Mr. Henry Ernest Dudeney and are relatively easy, the third problem is by me and is somewhat harder, and the fourth one, unfortunately I do not know by whom, and is the hardest of all, but if tackled appropriately, it can be found, really..

1) Two rooks (these pieces can move as many squares as possible, only vertically and horizontally) of opposite colors are placed randomly on an empty chess board, without one menacing the other. Two players are playing the game, one chooses the white rook, and the other one, the black rook (they do not know the positions of the rooks before choosing). The goal of the game being to capture the opponent's rook. Now each rook cannot pass through, or be on, the 'lines of fire' (that is, the squares that it controls) of the opponent's rook without being captured. This game can never end in a draw if both players know the winning strategy. Question: What is the winning strategy ?

2) We have the following board configuration:

White: Pawn: f7 King: g7 Bishop: f6

Black: Rook: e5

This was a game between two persons. It does not matter where the black king was, all we know is that black was completely lost, but the person playing black was very smart, and, of course, needed to catch a train. He could have abandonned, but instead he told the person playing white: 'Ok, I have to go now, you can finish the game for me, I will just leave my king on a square on the board, and then you can play all the moves in the world (black does not play, the black king stays where it is forever) until you checkmate my king. You can even leave my king in check with a piece (except the white king of course), while playing with another piece (this is of course not possible in a classic chess game). ' The person playing white agreed, but to his dismay, after much tries, he found it utterly impossible to checkmate the black king ! Question: on which square did the person playing black leave his king ?

3) We have the following board configuration:

White: Bishops: a2, b2 Black: Bishops: h3, d8

Now assuming the same rules as in Dudeney's first problem. That is, no bishop of a color, can pass through, or be on, a square attacked by a bishop of the opposite color without being captured. This may need a clarification: a white bishop, on white squares, cannot pass through, or be on, a square attacked by a black bishop, on white squares; but this white bishop on white squares is not at all dependent on the black bishop on black squares, etc. The goal being to capture both opponent's bishops. Question: White to play and win, how ?

4) We have the initial chess board configuration, with all pieces on their original squares. Now, playing a classic chess game, white plays on each consecutive move:

1. Pf2-f3 (Pawn from f2 to f3) 2. Ke1-f2 (King from e1 to f2) 3. Kf2-g3 4. Kg3-h4

After white plays his last move, Kg3-h4, black immediately plays and mates the white king. Again: this is a classic chess game which obeys all of its rules (of course, I doubt anybody ever played like that with white, but, well, we never know.. ).

Question: What are the complete moves of this short game ?

I'll print them out for the weekend...

Here are two puzzles more (from the initial position):

1. Black promises to play 'the same' moves as White do. For example: 1. e4 -> e5 2. La6 -> La3 and similar. How can White checkmate in 4 moves under this condition?

2. White checkmates in 8 moves. Conditions: - White uses only one piece for all moves. - Black doesn't move (only in case of check).

Have a nice weekend,

Sorry, La6 = Ba6.

But I don't know the author either.

well, we never know.. ).

The same can be said for Black

Hi,

Good puzzles. Let me tackle one at a time:

IF> 2) We have the following board configuration:

IF> White: Pawn: f7 IF> King: g7 IF> Bishop: f6

IF> Black: Rook: e5

IF> This was a game between two persons. It does not matter where the IF> black king was, all we know is that black was completely lost, IF> but the person playing black was very smart, and, of course, IF> needed to catch a train. He could have abandonned, but instead he IF> told the person playing white: 'Ok, I have to go now, you can IF> finish the game for me, I will just leave my king on a square on IF> the board, and then you can play all the moves in the world IF> (black does not play, the black king stays where it is forever) IF> until you checkmate my king. You can even leave my king in check IF> with a piece (except the white king of course), while playing IF> with another piece (this is of course not possible in a classic IF> chess game). ' The person playing white agreed, but to his IF> dismay, after much tries, he found it utterly impossible to IF> checkmate the black king ! Question: on which square did the IF> person playing black leave his king ?

Spoiler starts.... a1 a2 a3 a4 a5 a6 a7 a8 b1 b2 b3 b4 b5 b6 b7 b8 c1 c2 c3 c4 c5 c6 c7 c8 d1 d2 d3 d4 d5 d6 d7 d8 e1 e2 e3 e4 e5 e6 e7 e8 f1 f2 f3 f4 f5 f6 f7 f8 g1 g2 g3 g4 g5 g6 g7 g8 h1 h2 h3 h4 h5 h6 h7 h8 Spoiler ends......

Answer: b2

Analysis:

We can assume that the Black rook is captured, and the pawn gets promoted to the Queen. (Rook and Bishop are inferior, and the Knight is not sufficient if the BK is in the middle of the board). So, our task is to find a square where the BK cannot be checkmated with a K, Q and B.

1. Obviously, the BK cannot be on the edge (or corners) of the board, where a K+Q can checkmate.

2. If the BK is some arbitary dark square (let us say d4), the checkmate is possible by K-c2, Q-e6 and the B on the a7-g1 diagonal.

3. If the BK is on some arbotary light square (let us say e4), the checkmate is possible by K-e6, Q-f5, and the B on the a7-g1 diagonal.

It shows that the positions of WK and WQ is critical. The position of the WB is flexible.

(3) requires only to find two squares for the WK and WQ on the *same* side of the BK, WB anywhere. This is possible on any light square on the board.

(2) requires that the WK and WQ at *diametrically opposite* squares with respect to the BK, with one file/rank in between. The only two squares it is impossible are b2 and g7. Since the WK is already on g7, the answers hould b2.

(The presence of the Rook on e5 gives a hint that the WK shouls be somewhere on the a1-h8 diagonal. But, in the initial position, the WB could be placed on somewhere else , and the BR could be eliminated. Any idea what role the BR plays here?)

Happy Puzzling!

IF> 4) We have the initial chess board configuration, with all pieces IF> on their original squares. Now, playing a classic chess game, IF> white plays on each consecutive move:

IF> 1. Pf2-f3 (Pawn from f2 to f3) IF> 2. Ke1-f2 (King from e1 to f2) IF> 3. Kf2-g3 IF> 4. Kg3-h4

IF> After white plays his last move, Kg3-h4, black immediately plays IF> and mates the white king. Again: this is a classic chess game IF> which obeys all of its rules (of course, I doubt anybody ever IF> played like that with white, but, well, we never know.. ).

Could not find it. Probably, you meant the following one by Sam Lloyd:

1. f2-f3 e7-e5 2. Kf1-f2 h7-h5 3. Kf2-g3 h5-h4+ 4. Kg3-g4 d7-d5#

Note that the last move is Kg3-g4 and not Kg3-h4.

Please clarify.

IF> 1) Two rooks (these pieces can move as many squares as possible, only IF> vertically and horizontally) of opposite colors are placed IF> randomly on an empty chess board, without one menacing the IF> other. Two players are playing the game, one chooses the white IF> rook, and the other one, the black rook (they do not know the IF> positions of the rooks before choosing). The goal of the game IF> being to capture the opponent's rook. Now each rook cannot pass IF> through, or be on, the 'lines of fire' (that is, the squares that IF> it controls) of the opponent's rook without being captured. This IF> game can never end in a draw if both players know the winning IF> strategy. Question: What is the winning strategy ?

spoiler starts...

Suppose the two rooks are not initially on a common diagonal (i.e. not a bishop's move apart). Then the first player wins with the following simple strategy. Among the two legal moves that leave your rook a bishop's move away from your opponent's rook, choose the square that is closer to your opponent's rook. Your opponent will eventually be forced into the position where his rook is in the corner, yours is diagonally adjacent to it, and it is your opponent's move. Since your opponent cannot cross your 'lines of fire', he is obviously stuck.

If the two rooks are initially a bishop's move apart, then the second player wins by following the same strategy.

Note: there is no reason to give black the rook since white can always capture it.

b2. The bishop can't cover b1 nor a2 and neither can the king. The only piece left is the promoted piece. So what should white promote to? A bishop can't cover both these squares. The only square from which a rook could cover them is b2 but this is ruled out because the black king is already on b2. A knight could cover both squares from c3 but then no remaining piece could cover a1. The only choice left is a queen. The queen can cover both squares only from b2, b3, and c2. b2 is ruled out because the black king is on it. b3 and c2 are symmetrical so we only have to examine one of them. If the queen is on c2, then the queen must be protected by the king from d1, d2, or d3 (the bishop can't protect the queen). The bishop must cover both a1 and a3 which is impossible.

1.Ba3 etc.

Yes, I did figure this out but I'm too lazy to take the time explaining it and just to prove it, I'll mention that 1...Bf5 is met by 2.Bc4. and both 1...Bg4 and 1...Bf1 are met by 2.Bd5.

1. f3 e5 2. Kf2 Qf6 3. Kg3 Qxf3 (not the best move ) 4. Kh4 Be7

No no, the moves I gave are correct, on the fourth move, white plays Kg3-h4.. Although the problem you give is very interesting, and could point out the creator of the problem I gave, Sam Lloyd..

Hi Glenn, your answers to 1, 2, and 4 are correct For 3, you give 1. Ba3, but then black has 1. ... Bf1 which is strong. White can't play 2. Bd5 because it is in the line of fire of the bishop; and after for example 2. Bb3 or 2. Bb4, 2. ... Bc7! is strong, and after: 2. Bc5, 2. ... Bd3! is also strong. I will not say that 1. Ba3 is either wrong or right, but then, I need some more proof..

Oops! It does cross the line of fire. Strangely, I was also thinking that the a3 bishop could play down the entire length of the a3-f8 diagonal when it can't without crossing the line of fire. It must have been too late when I did this. At least I knew what White had to achieve in order to win.

You've convinced me that black wins after 1.Ba3

1. Be5 fails to 1... Bf1 2. Bb3 Be2. Hence, white's first move must restrict the h3 bishop, thus 1.Bd5.

The (relatively) complete solution is

1. Bd5! Bg4 2. Be5 .... Ba5 2. Be4 .... Be7 2. Bc3 Bd6 3. Be4 ............... Bf8 3. Bd4 Be7 4. Be4 .......................... Bg4 4. Be5 ............... Bd8 3. Bb4 Bc7 4. Be4 .......................... Bg4 4. Bc5 ............... Bg4 3. Bd4 .... Bc7 2. Ba3 Bb5 3. Be4 ............... Bg4 3. Bb4 ............... Bd8 3. Bb4 Bc7 4. Be4 .......................... Bg4 4. Bc5 ............... Bb8 3. Be4 Bc7 4. Bb4 .......................... Ba7 4. Bb4 Bb8 5. Ba5

At the end of each of these lines, the black's only moves (if any) that don't place his bishop on the same row or column as the opponent's like-colored bishop are to 'back away' towards an edge. White simply mirrors any such black moves with his like-colored bishop until black is forced to play one of his bishops onto the same row or column as his opponent's like-colored bishop (Forcing this is the point of the above lines. Also, the idea of always keeping an even number of 'approaching' moves available makes it a lot easier to see the logic of the above play.) Once this happens, white immediately moves his other bishop on the same row or column as the like-colored bishop. The play now is reminiscent of problem 1. After black moves, white always moves the corresponding bishop to the same row/column (if there is more than one such move, then choose the square that is closer to black's bishop). Both of black's bishops will be forced to the edge where they will run out of moves.