Chess game was created over many centuries and its rules changed several times. From a mathematical point of view, the movement of chess pieces and the shape of the board are very conditional. There are many different games on rectangular boards, the theory of which occupies a significant place in the mathematical literature. Only checkers games. more than a dozen are known: Russian, hundred-cell, Lasker checker, giveaway, corners, etc. Even modern chess has a number of varieties, mainly in non-European countries. For example, Gardner talks about Japanese chess (sogi), Chinese (qun ki), Korean (tian-keui). We will now focus on some chess games and problems (containing mathematical elements) in which the board or rules of the game differ from the usual ones.
Until the first check
. In this game, everything is like in real chess, only the winner is not the one who is “first” to give checkmate, but the one who is the first to declare check. With a normal initial position, White wins by force, and no later than the fifth move.
1. Nb1-c3. The knight threatens to attack e4, d5 or b5 with inevitable check, Black has only one answer:
1. … e7-e6(1. … e5 does not save because of 2. Nd5 and 3. Nf6 with check). Now after
2. Nc3-e4 Ke8-e7
3. Ng1-f3 the second knight comes into play with decisive effect.
3. …Qd8-e8(3. … d6 4. Nd4)
4. Nf3-e5 and check on the next move.
To “spice up” the game, you should change the starting position in some way, for example by moving the white pawn from c2 to c3, and the black pawn from c7 to c6. Now the first move 1. Nc3 is impossible, and a forced win is no longer visible, for example after 1. Qb3 d5 2. Qb4 Qd6! 3. Qa4 Bd7 4. Qh4 Nf6 the black king is well protected.
Two-move chess . In this game, each move of White and Black consists of two ordinary moves. This change in the rules allows us to prove the following non-obvious and unexpected fact.
When playing two-move chess correctly, White is at least guaranteed a draw.
Let's try to prove this by contradiction. Let White lose if both sides play best. After 1. Nb1-c3-b1 the initial position is preserved, and the first move already belongs to Black. In fact, now Black is playing White and, by assumption, is losing. Contradiction.
Everything seems correct. However, this proof is not entirely accurate. After White's first move, the position is indeed repeated, but the situation is different! So, after 1. ... Ng8-f6-g8 2. Nb1-c3-b1 White cannot yet demand a draw, but Black can, since 2. ... Ng8-f6-g8 leads to a threefold repetition of the original position when White moves. Thus, one cannot assume that after 1. Nb1-c3-b1 “Black plays White” - the sides have different possibilities. By the way, similar example You can also refer to the “50-move rule”.
It is noteworthy that this very subtle error in the proof was discovered by Academician A. N. Kolmogorov.
Let us now give a rigorous proof. We still believe that Black wins if both sides play flawlessly. We will play on two boards simultaneously. On the first board we will go 1. Nb1-c3-b1, and we will reproduce Black’s counter move on the second board from White’s side. Then we will repeat Black’s response on the second board for White first, Black’s move on the first for White on the second, etc. According to our assumption, Black wins and, therefore, the moment will come when on the first board they will declare checkmate with their next move to the white king. But then on the second board, when repeating this move 8a white, a position will arise in which checkmate is the floor of the chart black king! But Black played flawlessly on the second board as well. Contradiction.
Note that, unlike the clever deceiver who played one game with white and the other with black against Lasker and Capablanca (see Chapter 12), we acted absolutely honestly - both games played with the same color!
Our proof, as mathematicians say, is not constructive. We've proven that White can't lose at two-move chess, but we haven't figured out how he should play. Moreover, if it is shown that White is winning (as, for example, in the game "before the first check"), then, obviously, the first move 1.Nb1-c3-b1 loses! Thus, it is possible that our proof of White's win-win was carried out using a losing move!
Here is one of the common modifications of two-move chess. One player has a full set of pieces that move as usual, while the other has only a king and a few pawns, but they make two moves. The goal of the weaker side is to capture the enemy king. Anyone who gets acquainted with this game for the first time always chooses ordinary pieces and... quickly loses, even if the opponent only has a king and a couple of pawns. Apparently, the approximate equality of “strength” in this game is maintained if this king is accompanied by 5-6 pawns.
Chess without zugzwang . If in a certain position any move by White loses, then we say that they are in zugzwang (if any move by Black also loses, then the zugzwang is mutual). Chess without zugzwang differs from ordinary chess by the addition of one move - a move on the spot. There is no zugzwang in them, since you can always pass the turn of the move to your partner.
The above proof that when playing two-move chess correctly, White is guaranteed a draw, completely holds true for chess without zugzwang. However, unlike two-move chess, the search for immediate checkmate is hopeless here! Let us recall that in real chess, where White’s chances, judging by statistics, are noticeably higher, it is not at all proven that even with the best play he is guaranteed at least a draw.
The following game of tic-tac-toe is very popular among students of the Faculty of Mechanics and Mathematics. On checkered paper of any shape (even “infinite”), two people take turns putting crosses and toes. The winner is the one who is the first to place five of his icons in a row (vertically, horizontally or diagonally). Just like two-move chess and chess without zugzwang, it can be proven that even here a beginner with perfect play does not lose. True, the proof in this case is more complicated than in chess games.
Giveaways . This game is more popular in checkers, but its chess version is also very interesting. The winner is the one who gives away all his pieces first. Capture in this game is mandatory (including the king, which can be put into battle), and if several captures are possible, then the choice is arbitrary.
The ideas and combinations that arise in giveaways are quite original and completely different from those found in regular chess. Let's consider one simple endgame: a white pawn is on a2, and a black pawn is on b6 (there is nothing else on the board), white starts and loses (which means he wins at the giveaway).
There are only two pawns on the board, but look how many subtleties the position contains.
1. a2-a3! But not a2-a4, since the white pawn must be promoted only after the black one.
1. …h6-h5
2. a3-a4 h5-h4
3. a4-a5 h4-h3
4. a5-a6 h3-h2
5. a6-a7 h2-h1Л! It is the rook; during other transformations of the black pawn (into the queen, bishop and knight), White places the queen and either immediately or on the next move gives it away.
6. a7-a8С!! The white pawn becomes an even weaker piece, otherwise the black rook is immediately under attack. Now, on any of her moves,
7. Ba8-h1!, and White gets rid of the bishop.
Let's consider another position: White has a pawn on d7, and Black has a knight on f5 (there are no other pieces). How will the giveaway game end when White moves and when Black moves?
White wins in the giveaway game, regardless of the turn of the move. If their move, then after the transformation 1. d7-d8K! the horse quickly sacrifices itself. If Black makes the first move, then any jump of his knight should be d7-d8C!, and the bishop easily gets under the attack of the knight.
Problem of H. Klüver and K. Fabel. The white king is on f3, and black has two pieces - the king on d7 and the queen on c8. White starts and loses (wins in giveaways).
1. Ke4! Qd8!(otherwise the white king will come under attack already on the second move) 2. Kd4!, and on the next move the king commits suicide. Doesn't 1. Kg4 work? Qa6! Now it is impossible to move the king to f4, f5 and g5 (for example, 2. Kg5 Qf6! 3. K:f6 Ke6, and Black himself gives up both pieces), and other king moves lead to a draw - Black “sacrifices” the queen, after which the kings cannot get close to each other.
Numerous mathematical games and problems arise when moving to other chessboards. We have already encountered rectangular m×n boards (in particular, square n×n) for various values of m and n, as well as an infinite chessboard. If desired, most of the problems mentioned in the book can be formulated for these boards. Now we will look at chess games on boards that are obtained from ordinary ones using more complex mathematical transformations.
Projective chess . The rules of this chess game are based on the properties of straight lines, which are studied in projective geometry. In this geometry, any family of parallel lines intersects at some point at infinity. Accordingly, we introduce the infinitely distant fields of an infinite board: the field P x is the intersection of its horizontals, P y - its verticals, P 1 - diagonals parallel to a1 - h8, P 2 - diagonals parallel to a8 - h1. The projective board is obtained from the infinite by adding these four fields P x, P y, P 1, P 2.
The projective board retains many of the rules of regular chess, with the main addition being that a long-range piece can move to an infinitely distant square (given its mode of movement) and from there return to the final square of the board. Projective chess is especially popular among Yugoslav chess composers, with many projective problems composed by Petrovic. Let's consider one of them (Fig. 67).
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Rice. 67. N. Petrovich. Projective chessboard. White starts and checkmate in two moves |
First solution move: 1. Kh2-g1! Now the black king has several answers. If he goes to e4, then the white queen gives mate, moving off to infinity through a5: 2. Qc5-R x mat. Indeed, from square P x the queen attacks the black king and holds all the squares around it: e3, f3 - through b3; d4, e4, f4 - through b4; d5, e5, f5 - through a5. Move 2. Qc5-R x mate and when 1. … Kf4-f3. In this case, the queen holds squares e4, f4, g4 through h4, e3, f3, g3 - through h3, and e2, f2, g2 - through h2 (the white king prudently left h2).
When the black king retreats to the g-file, as well as when 1. ... d3-d2 mates 2. Qc5-R 1(the queen goes to infinity along the diagonal c5 - a3). For example, after 1. ... Kf4-g5 2. Qc5-P 1 squares f4, g5, h6 the queen holds through c1, square f6 - through a1, f5 - through h7, g4, h5 - through d1 and square h4 - through e1.
It remains to consider the moves of the black knights. For any knight move d6 should 2. Qc5-R 2 checkmate, and for any knight move c7 - 2. Qc5-R y checkmate (in the first case the queen goes to infinity through a7, and in the second through c8).
When solving the problem analyzed, all four fields at infinity were used. By the way, in the initial position after 1. Qc5-R x the black king hides on g5, and after 1. Qc5-R 1 - on e4, from the square R 2 the queen does not even give check, and there is no move Qc5-R y at all.
All the boards we have considered so far, like the usual chessboard, are flat. Let us now dwell on some spatial boards.
Volumetric chess . They are played on a three-dimensional m×n×k board. In ch. 5 showed the knight's routes across all squares of a 4x4x4 board and along the surface of an 8x8x8 board. The next, rather difficult problem concerns the placement of rooks on a three-dimensional n×n×n board.
What is the minimum number of rooks that should be placed on the n×n×n board so that they threaten all other squares of the board?
In fact, here you need to find the number of “rook-sentries” dominating on a three-dimensional board n×n×n.
It turns out that it is equal to n²/2 for even n and (n² + 1)/2 for odd n. In particular, to “guard” an 8x8x8 board, it is enough to have 32 rooks. The number of independent rooks on the n×n×n board is n² (but there are n rooks in each layer of the board). On an 8x8x8 board, it is possible to place 64 rooks so that they do not threaten each other and at the same time keep all the free squares of the board under fire. Our problems of dominance and independence of rooks on an n×n×n board can be formulated as follows in terms of linear algebra.
Let's consider the set of all three-dimensional vectors (t 1, t 2, t 3), the components of which take one of the values 1, 2, ..., n (there are n³ such vectors in total). What is the minimum number of vectors that should be selected from this set so that each of the remaining vectors has at least one common component with at least one of the selected ones? What is the maximum number of vectors that can be chosen such that no two of them have any common component?
The first question is equivalent to determining the dominance number of rooks on an n×n×n board, and the second is equivalent to determining the independence number. Thus, the answer is: in the first case there are n²/2 or (n² + 1)/2 vectors, in the second case there are n² vectors. Consideration of the last problem suggests the following generalization.
Multidimensional chess . The board fields for playing such chess are multidimensional cubes 1×1×…×1. In this terminology, our rook problems can be generalized to a k-dimensional chessboard.
Let's consider the set of all k-dimensional vectors (t 1, t 2, ..., t k), the components of which take one of the values 1, 2, ..., n (there are n k of such vectors in total). What is the minimum number of k-dimensional vectors that should be selected from this set so that each of the remaining vectors has at least one common component with at least one of the selected ones? What is the maximum number of k-dimensional vectors that can be chosen such that no two of them have any common component?
The solution to this problem is unknown. Similar problems of dominance and independence on multidimensional boards can be posed for other chess pieces. The mentioned article by Vasiliev shows the connection between problems of this type and some questions that arise in information theory (in its section called coding).
Cylindrical chess . Problems on cylindrical boards are especially popular among chess composers. From an ordinary chessboard you can build, generally speaking, two cylindrical ones. A vertical cylindrical board is obtained by gluing the vertical edges of a regular board (Fig. 68, a), and a horizontal one is obtained by gluing the horizontal edges (Fig. 68, b). It is interesting that if one vertical (or, accordingly, horizontal) is cut out, then on a cylindrical board the elephant becomes a chameleon - it turns from a white-squared to a dark-squared one, and vice versa.
When moving to a cylindrical board, some problems that can be solved on a regular board can no longer be solved. Thus, in Chapter 8 we showed that it is impossible to arrange eight fairways that do not attack each other. Note that on a cylindrical board, a king and a rook cannot always mate a lone king. On the other hand, cylindrical boards also open up new possibilities.
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Rice. 69. White starts and gives mate in two moves: |
In the problem in Fig. 69 on a regular board everything is simple - 1. Ra5:a6 Kb1-c1 2. Ra6-a1 mat. But on the cylindrical 1. Ra5:a6 it does not work, since after 1. ... h7:a6! the rook is lost. If the rook moves away from a5, then Black will advance the a-pawn and there will be no mate. What to do? It turns out that it solves 1. Ra5-a5!!- the rook goes around the circle and returns to its original place! The rest is simple: 1. … Kb1-c1 2. Ra5-a1 mat.
The problem in Fig. 70 is notable for the fact that each of the three boards (regular and two cylindrical) has its own solution, which does not work in the other two cases: a) 1. Qe2-e8 mat; b) on a vertical cylinder 1. Qe8 does not mate due to answer 1. ...Ka8-h7!, but only leads to the goal 1. Qe2-g8 checkmate (the white queen followed the route e2-a6-h7-g8); c) on a horizontal cylinder 4. Qe8 also gives nothing, due to 1. ... Kra8-a1!, but solves 1. Qe2-a2 mat!
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Rice. 70. Bondarenno. White gives mate in one move: |
Toroidal chess . A toroidal board (Fig. 68, c) is obtained by double gluing the edges of a regular board (see arrows in Fig. 68, a, b). On such a board, even a queen and king cannot mate a lone king - there simply is not a single mating position here.
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Rice. 71. Z. Mach. Toroidal board. White starts and checkmate in four moves |
Let's solve the problem in Fig. 71. After
1. Qf5-h7! Black has two answers at his disposal:
A)
1. … Ke8-f8(fields d1, e1 and f1 are controlled by the white king with e2 - the horizontal cylinder rules apply on the torus!)
2. Qh7-g6 Kf8-e7
3. Ke2-e1 Ke7-d7(squares d8 and f8 are held by the white king with e1)
4. Qg6-e8 mat!;
b)
1. … Ke8-d8
2. Qh7-c7+ Kd8-c8
3. Nb5-b6!(the horse walks along the torus as if along a vertical cylinder!)
3. … Ke8-f8
4. Qc7-e1 mat! (squares f7 and g8 are held White horse, and the rest are the queen).
This list of chess games on various boards, obtained from a regular one using geometric transformations, can be continued further. There are two-on-two boards (the so-called quadruple chess is played on them) and “three-on-three” (here the winner is the one who eats both opponents’ kings). If desired, you can also build spherical and conical boards. A funny board - spherical in shape - is depicted on the cover of the book. As an exhibit, she participated in an exhibition of French avant-garde artists.
In chess composition, problems and games with unusual rules, on non-standard boards and with unusual pieces, belongs to the genre of fairy-tale (or fantastic) chess. The founder, popularizer and largest author of fairy-tale problems is the English problem specialist T. Dawson, some of whose problems we met in our book. In the 30s and 40s, Dousoi published a special magazine dedicated to fantasy chess, and then wrote a number of books on this topic. In total, Dawson compiled more than 4,000 (!) fabulous problems, which certainly represents an absolute record. Most of the ideas of this fascinating chess genre are contained in the wonderful book by A. Deakins, “A Guide to Fairytale Chess.”
We have already talked about some chess games with unusual rules, and also listed a number of unusual boards. Let us now dwell on the fairy-tale figures that have gained the greatest popularity.
A number of fairy-tale characters arise from combining the usual moves of a rook, bishop and knight. There are four possible combinations: rook + bishop, rook + knight, bishop + knight, rook + bishop + knight. In the first case, we get a real chess piece - a queen. The piece that combines the moves of the rook and knight is called the chancellor, and the bishop and knight are called the centaur. The centaur is generally stronger than the rook, but, as was shown in Chap. 10, there are boards on which their strengths are equal. And finally, a piece that moves like a rook, bishop and knight at the same time is called a maharaja, or Amazon (already discussed in Chapter 8). This is a very powerful piece, much stronger than the queen. The next game has the same name as the fairy-tale figure itself.
Maharajah . One player has a full set of pieces standing in their original places, while the other has only one maharajah, whom he places on a random field. The Maharajah loses if he is captured, and wins if he checkmates the enemy king.
In this game, pawns are forbidden to promote, since otherwise the winning is too simple - it is enough to move both outer pawns into queens, after which three queens and two rooks easily surround the maharajah. With the reservation made, the maharajah puts up stubborn resistance, and quickly wins against an inexperienced player (here the same situation occurs as in the fight of a full set of pieces against the king and pawns making two moves each). And yet, the one who plays with a full set of pieces has a forced win. Gardner proposes a plan to encircle the Maharajah, consisting of 25 moves. However, the goal is achieved at least ten moves earlier!
Ignoring the Maharajah's movements, White makes the next 14 moves in a row: 1-14. a4, h4, Ra3, Rh3, Nc3, Nf3, Rb3, Rg3, d4, Qd3, Qe4, Rb7, Qd5, Rg8. It is easy to check that with these moves the Maharaja could not give checkmate or capture a white piece. Now he has only two free squares - a6 and f6: on a6 he dies after 15. Bg5, and on f6 - after 15. e4.
Various fairy-tale figures are obtained from the “generalized horse” (a, b) by choosing certain values of a, b (see Chapter 4). The horse (1, 3) is called a camel, (1, 4) is a giraffe, (2, 3) is a zebra. If one of the numbers a, b is equal to zero, then we get a rook moving a fixed number of squares. If a = b, then we have a bishop with the same property. Kongo, who makes several jumps in a row in one turn, is awarded the “rank” of a horseman. Interesting game, in which the same figure is used both as a horse and as a camel, the following problem is devoted.
There is a piece in the corner of the n×n (n ≥ 4) board. The two take turns. One plays this piece like an ordinary knight, but with a double move, and the second plays like a camel. The first one strives to place a piece in the opposite corner of the board, and the second one tries to interfere with it. How will the game end?
In this somewhat strange competition between a horse and a camel (or rather, it would be more accurate to say: a chameleon, turning into one figure and then into another), the horse emerges as the winner! This follows from the following considerations. If our piece stands on a diagonal passing through the original corner square of the board, then for any retreat of the camel from the diagonal, the knight returns to it, and moves at least one square closer to the goal, or even immediately gets to the desired corner.
The following game and problems for it were proposed at the All-Union Olympiad for Schoolchildren (Yerevan, 1974)
Cat and mouse . One player has one piece - a mouse, the second player has several pieces - cats. The mouse and cats move the same way - on the same square vertically or horizontally (that is, they are obtained from the knight (a, b) with a = O, b = 1). If the mouse is on the edge of the board, then in its next move it jumps off the board and runs away from the cats; If a cat and a mouse land on the same field, then the cat eats the mouse.
The game is on chessboard, and the players take turns, and the second of them moves all their cats at once (in any direction) in one move. The mouse starts. She tries to jump off the board, but the cats want to eat her before that.
A. Let there be only two cats, and the mouse is not on the outermost field of the board. Is it possible to place cats on the edge of the board so that they can eat the mouse?
b. There may be three cats, but for the first time the mouse makes two moves in a row. Prove that the mouse will run away from the cats, no matter how the pieces are placed at first.
A. Let's draw a diagonal across the field on which the mouse stands and place cats at its ends. After the mouse move, the cats must move so that all three pieces are again on the same diagonal, and the distance between the cats is reduced by one field (diagonally). This strategy will allow the cats to eat the mouse.
b. Let's draw both diagonals of the board across the field on which the mouse stands. If the field is not extreme (otherwise the mouse immediately jumps off the board), then these diagonals divide the board into four parts. Since there are three cats, there are none inside one of the parts. Let's draw a segment (horizontal or vertical) connecting the mouse to the edge of the board inside this part. It is easy to see that if the mouse goes straight along this segment to the edge of the board, then the cats will not catch up with it.
As we know, a maximum of 32 knights can be placed on a chessboard without threatening each other. The maximum number of “peaceful” camels is 16, i.e. they can also occupy half of the entire board (checkerboard).
In Fig. 72 they can be placed on the fields with all even or all odd numbers. Thus, this drawing provides a solution to two problems on the chessboard at once. More detailed story about chess (in particular, the arrangement of pieces before the start of the game) can be found in Gardner.
In conclusion of the chapter - about a few more fairy-tale figures that do not resemble anything at all!
The cricket walks like a queen and jumps over its own and other people's pieces, stopping immediately after them. The lion, unlike the cricket, lands on any field behind the jumping figure.
There are neutral pieces that can be played by both white and black. A piece that makes a move only with a capture; called hitting. A beating knight is called a hippopotamus, and a beating queen is a dinosaur. The diplomat figure does not move, but it cannot be taken either. Moreover, around the diplomat, figures of the same color are inviolable! And the kamikaze (suicide) piece is removed from the board along with the captured piece!
Until now we have been talking exclusively about fairy-tale figures. However, there are many varieties for pawns as well. When a chameleon pawn is captured, it turns into the same piece, but of its own color. The superpawn moves to any number of squares in a straight line and attacks to any number of squares diagonally. The taxi pawn moves both forward and backward. Finally, once in the game a pawn can be allowed to be promoted to " atomic bomb"! Immediately after its appearance, this figure is placed on any square of the board and within a given radius destroys everything around it.
More details about projective chess can be found in the article “Projective Chess” (Kvant, 1974, No. 3).
A detailed discussion and solution to this problem is given in the article by N. Vasiliev “Arrangement of cubes” (Kvant, 1972, No. 4).
A. Dickins. A. Guide to Fairy Chess. Richmond, 1969.
S. Golomb. Of Knights and Cooks, and the Game of Cbeskeis. - "J. Recreat. Matb.”, 1968, N 1.
Would you like to have a wonderful exercise for your mind? Then start playing the popular one intellectual game"Chess on the boards" and you will find an excellent use of your intelligence, ingenuity and logical thinking. Mathematical calculations, geometric combinations and phenomenal memory - all this will be useful to you in a real battle between two armies of white and black leaders, which broke out on a small chess field.
The rules and essence of this fun are well known to everyone. At your disposal are various figures that move in their own way. Here are the king and queen, knights, officers, rooks and of course pawns. The task of your brave army is to protect your ruler from enemy attacks and conquer enemy territories. In the game of Chess on Boards, the pawns are the first to enter the battle.
They only move forward two squares if they are in their own half of the field, and one if they are in the opponent’s half. They can hit diagonally. The horse walks in a “g” shape and also destroys enemies. The rook moves in all directions in a straight line, and the officer moves along diagonals. By clicking on the piece you want to move, the computer will give you a hint by highlighting the corresponding areas of the field where you can move in green.
To successfully play “Chess on the boards” you need to carefully consider your moves, weigh every choice, and be able to sacrifice less significant characters in order to save more important ones. You can also set up cunning traps for your opponent to get rid of his warriors who are dangerous to you. Good luck to you and vivid impressions!
On a checkered chessboard measuring 8 by 8 cells, you can play not only chess and checkers. There are many more games that will help you spend free time fun and useful.
One of them is the game Corners. Children can play it starting from 3-4 years old.
Players line up checkers in the left corner (each on their own side) of the chessboard. This place is called HOUSE.
You can play with 9 checkers, lining them up in a three-by-three square.
You can use not 9, but 10 checkers, building triangles from them.
You can use more checkers by building the original HOUSE into a three by four or four by three rectangle. Or even a four by four square. But a large number of checkers creates “pandemonium” and the game drags on for a long time.
Purpose of the game
The goal of the game is to rearrange the checkers in such a way as to quickly occupy all the cells of his HOME with your checkers.
Basic rules of the game.
You can only move one checker in one move.
You can only move horizontally or vertically (right, left, up, down) one cell.
You can also jump over your own and other people's checkers.
The number of jumps can be any. The main rule is that each jump is made only through one checker. You cannot jump over two adjacent checkers. Here is a picture of a cage jump c1 in a cage g7 can be done in one step.
The "compulsory move" rule. If one of the players has removed all his checkers from his HOME, the second is obliged to make moves only with those checkers that he has not yet removed from his HOME. This rule prevents the deliberate blockade of enemy checkers.
The “forbidden strategy” is copying all of your opponent’s moves. Naturally, in this case the game ends in a draw.
The winner is the one who was the first to occupy all the squares of the opponent's HOUSE with his checkers.
In this picture, Black won with a clear advantage!
As in any gambling game, in the corners there is an opportunity to play not only for wins and losses, but also for the score. When playing for a score (prizes, bonuses), the losing player ends the game by making moves and counting them. How many moves are needed to move all the checkers into the house, the number of points he lost.
The opportunity to play any free games, volcano, slot machines, and even corners can be found in online casinos or on many other gaming sites on the Internet.
“Games have some of the characteristics of works of art,” wrote Aldous Huxley. - With their simple and clear rules, they appear before us as islands of order in the chaos and confusion of empirical experience. When we play them ourselves or just watch others play them, we move from the incomprehensible universe of this reality into a small, strictly ordered world created by man, where everything is clear, purposeful and easily understandable. The spirit of competition, mixed with the inner charm of games, makes them even more exciting, while the thirst for winning and the poison of vanity, in turn, give special sharpness to the competition.
Huxley spoke about games in general, but his remarks sound with particular force in relation to mathematical games on a special board like a chess board, where the outcome of the game is determined not by sleight of hand or blind play of chance, as happens when playing dice or cards, but by pure thinking. These games are as ancient as civilization and as varied as the wings of butterflies. If we consider that until recently these games served only to “relax” and refresh the mind, then we cannot help but admit that humanity has spent a fantastic amount of mental energy on them.
Nowadays, the position of games has changed dramatically: they have taken a prominent place in the theory of computers. It is quite possible that self-learning machines that “know how” to play checkers and chess will be the predecessors of a self-improving electronic brain capable of reaching unprecedented heights in the development of its abilities.
As far as we know, mathematical games on special boards appeared in Ancient Egypt. However, very little information about them has reached us, since it can only be gleaned from works of art, and the Egyptians, by tradition, depicted everything only in profile. True, some of these games were found during excavations of ancient Egyptian burials (Fig. 202), but they cannot be considered math games in the strict sense of the word, since they contain an element of chance.
Rice. 202 The game "senet", found during excavations of an Egyptian burial of 1400 BC. e. Moving figures are visible.
A little more is known about the games Ancient Greece and Rome, but the first record of the rules of the game of the type we are interested in appeared only in the 13th century, and the first books only in the 17th century.
Like living organisms, games develop, multiply, and new species appear in the process of their development. Some simple games, such as the game of tic-tac-toe, may remain unchanged for centuries; others, after a short period of flourishing, disappear forever. A striking example of a kind of dinosaur among entertainment should be considered rhythmomachy - an extremely complex number game that medieval Europeans played on a double chessboard measuring eight squares by sixteen with pieces shaped like circles, squares and triangles. The first information about it is found in the chronicles of the 12th century, and in the 17th century, Robert Burton in his book “The Anatomy of Melancholy” mentions rhythmomachy as one of the popular games in England. Many learned treatises have been written about rhythmomachy, but now no one plays it, except perhaps some mathematicians and specialists in the history of the Middle Ages.
In the United States, the most popular games that require a special board are, of course, checkers and chess. Both have a long and fascinating history, their rules from time to time undergo unexpected “mutations” (it is hardly an exaggeration to say that almost every country had its own national versions of these games).
Nowadays, American checkers are no different from English ones, but in other countries there are numerous different versions of checkers. Most European countries mainly adopt the so-called Polish checkers (actually invented in France). They play Polish checkers on a hundred-square board, each opponent has twenty pawns, and you can take a pawn either by moving forward or by moving backward. Pawns with a crown (called queens rather than kings, as in chess) can move in the same way as a bishop in chess. After capturing an enemy pawn, such a “crowned” pawn can be placed on any free square behind the captured pawn. The game is very popular in France (where it is called “dames” - “queens”) and in Holland, and many theoretical works are devoted to it.
In Canadian provinces with speaking populations French, and in some areas of India, Polish checkers is played on a board measuring twelve by twelve squares.
German checkers (Damenspiel) are in many ways reminiscent of Polish ones, but they are usually played on an English sixty-four square board. Very close to the German version of the “small Polish” game, known in Russia under the name “Russian checkers”. Spanish and Italian versions of the game are closer to English checkers. Turkish checkers (“queen”) is also played on a board measuring eight squares by eight, but each opponent has sixteen pawns that occupy the first and third rows of squares, counting from the corresponding edge of the board. Pawns can move forward, backward, right and left, but not diagonally. There are other significant deviations from both the English and Polish varieties of checkers.
The name of the inventor and the date of origin of chess, the rules of which are also incredibly varied, are unknown. The game is believed to have originated in India sometime around the 6th century AD.
Although international chess currently follows the same rules, there are many excellent variations of the game in non-European countries that share a common origin with international chess. In modern Japan, Sogi, Japanese chess, has as many enthusiastic followers and admirers as the game Go, although in Western countries only the latter is known. Sogi is played on a board measuring nine squares by nine. Each opponent has twenty pieces.
At the beginning of the game, the pieces are lined up in three rows. Just like in Western chess, the game is won when a piece that moves similarly to the king in our chess is checkmated.
Sogi has an interesting feature: the player can put the opponent's pieces back on the board and use them as his own.
A game of Chinese chess (qun ki) also ends when a piece whose moves resemble those of a king in Western chess is checkmated, but the rules of this game are very different from the rules of Japanese chess: thirty-two Chinese chess pieces stand at the intersections of vertical and horizontal lines A 64-square board divided down the middle by a horizontal row of empty squares called a "river". In the third version of the game - Korean chess (tian-keui) - the pieces are placed at the intersections of vertical and horizontal lines, and the board is marked in the same way as when playing Chinese chess. The only difference is that in Korean chess the “river” is not specifically marked out, so the board looks like a chess board measuring eight squares by nine. There are the same number of pieces as in Chinese chess, and they are called the same (except for the “king”).
The formation of the pieces at the beginning of the game in Chinese and Korean chess is also the same, but the rules and relative value of the pieces are different in both games. Fans of each of the three eastern varieties of chess believe that any of the other two variants of this game and Western chess are in many ways inferior to their chosen version of this ancient game.
The rules of playing “Martian” chess (“jetan”) were explained in the appendix to his novel “Chess Players from Mars” by Edgar R.
Burafs. In this exciting game you are supposed to play on a hundred-square chessboard with unusual pieces and according to completely new rules. For example, the princess (a figure roughly equivalent to our king) has the right to “escape” once per game, which allows her to walk any distance and in any direction.
In addition to the numerous national varieties of chess, modern chess players, tired of the orthodox game, have invented many of the most bizarre games, known as “unusual” or “fantastic” chess. Among the many games of this type that can be played on an ordinary board measuring eight by eight squares, we mention only two-move chess, in which each of the players takes turns making two moves in a row; a game in which one of the opponents has no pawns or, conversely, instead of a queen there is an extra row of pawns; cylindrical chess, in which the left edge of the board is considered to be glued to the right edge (if the board is twisted half a turn before “gluing”, then the game is called “chess on the Mobius strip”); chess with moving pieces, in which any piece can be placed on a rook and moved to another square. Dozens of new pieces were invented, such as the chancellor (combining the moves of a rook and a knight), the centaur (moving as both a bishop and a knight) and even neutral pieces (for example, a blue queen) that both opponents could move. (In L. Padgett’s science fiction novel “Unusual Chess,” the war is won by a mathematician, whose favorite pastime is the same fantastic chess that we just talked about. His mind, accustomed to breaking the usual rules, easily copes with an equation that seems too complex for him more brilliant, but also more orthodox-minded colleagues.)
One of the older, but no less entertaining varieties of fantasy chess, which serves as an excellent introduction to more serious games, is played as follows. One of the players places his sixteen pieces as usual. The other player has only one piece, which is called the “maharaja”. You can use a queen as a maharaja, but this “unique” piece moves both as a queen and as a knight.
At the beginning of the game, the Maharajah is placed on any square that is not under the attack of a pawn, after which the opponent makes his first move.
The Maharajah loses if he is captured and wins if he checkmates the opponent's king. It is prohibited to replace pawns that have reached the opposite edge of the board with queens or other pieces.
Without this clause, it would not have cost anything to defeat the Maharajah: it would have been enough for both rooks' pawns to reach the opposite edge of the board and become queens. Since both of these pawns (as well as the others) are protected, the Maharajah cannot prevent them from becoming queens, and with three queens and two rooks, the game is not difficult to win.
It may seem that even with this stipulation, the maharajah's chances of winning remain rather low, but his mobility is so great that if he moves actively and aggressively, he is often able to checkmate his opponent soon after the start of the game. Sometimes the maharajah clears the board of all the opponent's pieces and drives the king, who is left completely alone, into a corner.
Hundreds of such games have also been invented, which, although they use an ordinary chessboard, have nothing in common with either checkers or chess. One of best games This type, in my opinion, is a now forgotten game called “reversi”. For this game you need to take 64 chips, the top side of which has one color, and the bottom side has another color (for example, black and red). A rough set of chips can be made from a piece of cardboard painted on one side, cutting out small pieces from it and gluing them together.
It's even better to glue together a set of chips from inexpensive checkers, buttons, etc. The joy that a new game will bring to your family members will reward you for the hassle associated with making the chips.
At the beginning of the game in reversi, the board is empty. One of the players takes 32 red chips, the other - 32 black chips. Players take turns placing one chip on the board according to the following rules.
1. The first four chips must be on the four central squares. Experience shows that it is advantageous for the first player to place the second chip next to the first (as in Fig. 203) or above or below it, but not diagonally, although this is not necessary.
Rice. 203 Start of the game in reversi. The cells are renumbered for easier description of the game.
For the same reasons, it is wiser for the second player not to place his piece diagonally from the opponent’s first piece, especially if the opponent is a beginner. This will give the first player the opportunity to take an unfavorable position on the diagonal during the second move. If experts play reversi, then the initial position has the form shown in Fig. 203.
2. Having filled the four central cells, players continue to place one chip on the board at a time. Each piece must stand on a cell whose side or corner is adjacent to the cell occupied by the opponent’s piece. In addition, the new chip must be located in the same vertical or horizontal row with other chips of the same color. Between chips of the same color there can be enemy chips, but there should not be empty cells. In other words, the new piece must be placed so that it is one of two “friendly” pieces located on either side of one enemy piece or a chain of enemy pieces. Once “encircled”, enemy pieces are considered captured, but they are not removed from the board, but are turned over, “turning” them into “friends”. They are, so to speak, subjected to such “processing” that they change owners. During the game, chips cannot be removed from the board, but they can be turned over as many times as desired.
3. If, having placed the next chip, the player flanks not one, but several chains of enemy chips, then the chips must be turned over in all chains that are “encircled.”
4. You can capture an enemy piece only if, during your next move, it (or the chain of enemy pieces in which it is included) ends up sandwiched between two of your pieces. Chains of pieces that are bordered on both sides by enemy pieces for some other reason are not considered captured.
5. If a player cannot go, he misses his turn. He must skip moves until he can make the next move in compliance with all the rules.
6. The game ends when either all 64 cells are filled, or none of the players can make any more moves (this can happen if a player has lost all his chips or if he cannot make another move without breaking the rules games). The winner is the one with the most chips on the board.
Let us explain the rules with two examples. In the position shown in Fig. 203, Black can only go to squares 43, 44, 45 and 46.
In each case, they take and turn one light chip. In Fig. 204 light moves to cell 22 immediately turn six black chips standing on cells 21, 29, 36, 30, 38 and 46.
Rice. 204 Having made the next move, the “light” ones win six chips from the “black” ones.
As a result, the board, which was previously dominated by black, noticeably brightens. Dramatic transitions from one color to another are common in this unusual game, and often before the final moves are made it can be difficult to tell which player has the better position. The player with fewer chips often has a stronger positional advantage.
Some tips for beginners. At the beginning of the game, try to limit your moves to the sixteen central squares as much as possible. In particular, you should aim to occupy squares 19, 22, 43 and 46. By being forced to leave this square, the first player is usually at a disadvantage. Outside the sixteen central squares, the greatest advantages are provided by the corner squares of the board. To prevent your opponent from occupying them, it is unwise to place your chips on squares 10, 15, 50 and 55. The next most advantageous squares after the corners are squares C, 6, 17, 24, 41, 48, 59 and 62. ). Moves that allow the enemy to occupy them should be avoided whenever possible.
Any player who has risen above the level of a beginner can formulate the remaining, deeper rules of the game in reversi on their own.
There was almost no analysis of the game in reverse. Even when playing on a four-by-four board, it is difficult to tell which player (if any) has an advantage over their opponent. Readers can try their hand at solving the following problem: can it happen that on the tenth move one of the players wins the game, turning all the opponent’s chips into his own?
The honor of the invention of reversi was challenged by two Englishmen - Lewis Waterman and John W. Mollett. Each of them reviled his opponent in every possible way and called him a deceiver. At the end of the eighties of the last century, when the game of reversi was extremely popular in England, both rivals vied with each other to publish manuals for the game and even founded (each separately) own companies, which produced boards and chips.
It doesn't matter to us who invented reversi. Another thing is important: in reversi the complexity of combinations is combined with the amazing simplicity of the rules, and this game in no way deserves to be forgotten.
When playing Maharaja, the participant who plays with a full set of traditional shakmat pieces can always win (of course, if he does not make rash moves).
Most effective plan The victorious campaign against the Maharajah was invented by William E. Rudge. If there are no internal contradictions in Raj's reasoning (and, apparently, this is the case), then the Maharaja can always be taken in no more than 25 moves.
Now the Maharaja (M) is forced to retreat to the seventh or eighth horizontal:
This move is only made if M is on the g7 square. He forces M to leave the black diagonal running from the lower left corner of the board to its upper right corner, thereby opening up the possibility of the following moves:
This move is only needed if M is on the f8 or g8 square.
This move is made only if M is on the g8 square.
The next move is to take the Maharajah.
Moves 1–4 and 5–9 can be rearranged, maintaining the sequence of moves within each group. The need for such a rearrangement arises when M blocks some pawn. Moves 15 and 22 are idle, they are needed only in those cases when M is on the already mentioned fields. Move 23 is made if necessary, only to force M to move to the left half of the board.
Relatively early history Little is known about reversi. Apparently, the game first appeared in the seventies of the last century in London under the name “Capture”. They played it on a board shaped like a cross. The second version of the game, which used a regular chessboard, was called “Capture, or a game of reversal.” By 1888, the name reversi was finally established for the game, and in England it became almost a craze. Articles about new game in the spring of 1888 the London newspaper Queen was published. Later, the London firm Jacques and Son released a version of the game called Royal Reversi. It was played with cubes whose edges were colored various colors. A description of the Royal Reversi and a view of the board can be seen on pages 621–623 of the Handbook of board games"Professor Goffman" (aka Angelo Lewis), who has long become a bibliographic rarity.
Later, reversi and games close to it appear on store shelves under a variety of names. So, in 1938, the game “Chameleon” was released - one of the varieties of royal reversi, and in 1960 reversi was released under the pseudonym “Las Vegas Rival”. The game, "Exit", which appeared in England in 1965, is nothing more than reversi, played on a board with round cells. The lid for each cell can be made red, blue or white (neutral), which allows you to do without chips.
Is it possible, playing reversi, to win the game in ten moves by turning all the opponent's chips into chips of your own color? Yes, you can. In the journal version of this chapter, I indicated a solution that seemed to me to be the shortest of all possible in reversal games (something similar to perpetual check in ordinary chess): the first player wins on the eighth move. (I found the description of the game in one of the old books on reversion.) But two readers managed to come up with even shorter solutions.
D. G. Peregrine sent the following game in six moves:
The solution found by P. Petersen is slightly different from it:
Maharaja Rules of the game Maharaja 1. White must catch and destroy the Feryaz of all kinds, not letting him near his own King. But we warn you that the Maharaja can single-handedly checkmate the opponent’s King. 2. Of course, if Pawns were allowed to transform into Queens, even ordinary ones, they would easily cope with the Maharajah. Therefore, the only restriction for Pawns is that they cannot transform into Queens or other pieces. You can walk on pawns. 3. The task of the Maharaja is to give MAT to the King.
Checkmates - chess and checkers together The initial arrangement of chess pieces, as in regular CHESS. This makes it possible to occupy the CENTER with a large number of PAWNS. That's already a plus. All the pieces made their moves as CHECKERS. Although they could do it in CHESS. A QUEEN at the beginning of the game is already both a QUEEN and a KING. Capture can be done in CHESS and CHECKER. Moreover, if there is an opportunity to hit like CHECKER, then capturing is MANDATORY! In chess, they have the right to choose - to HITTLE or NOT TO HITTLE!
During CHESS “eating” of pieces, a situation may arise when it is possible to beat in CHESS. Then this move can be added to the CHECKER “eating”. But the chess move will be the last! Be careful with the King! The king wants to “eat” the f 2 rook, but there is no need to get carried away, especially since chess captures are not necessary. You can also beat with a rook. 1. Kg 1: f 2? A blunder and the game will end immediately. “Enterment” follows! 1. . Ce 5–g 3! and then if you want, hit it like a chess, you want it like a checker (must!) - they are waiting for the king. . .
Only PAWNS can become QUEENS. But other pieces cannot become KINGS, even if they reach the last line, like CHECKS. Although you can agree and try such transformations. The king can only be beaten with a CHESS move; “in CHESS” the piece must stop and declare a respectful CHECK. The winner is the one who eats the opponent’s King “by CHESS” or “by CHESS” who delivers MAT. Maybe we forgot, so you can add your own rules to the game! Actually, the game is terribly interesting, although in many ways unusual and unusual.
Two-Move Chess Look at the board. On one side of the board is MATE to the Black King, but the game is called “TWO-MOVE CHESS”. Therefore black plays 1 -2. . Cre 8:e 7! and Cre 7:e 6! And there were no horns or legs left of the white ones. Black victory!
Rules of the game of two-move chess The one who eats the opponent's King wins. There are no checkmates or checkmates in the game of TWO MOVES. Or rather, they exist, but no one attaches serious importance to them. The main thing is a counterattack on the King!!! Ate the king and full order! You can make two moves in a row with one piece or pawn, or two different pieces during a move. Whites start first. But they are only allowed to make one move! Otherwise they will get a very big advantage. Black responds with two moves, and then each side makes two moves until the end of the game. Look at the position. It could have happened after White's second couple of moves, if he had been allowed to make two double moves at once.
Chess transformers Have you seen chess pieces that can transform? You will say that this is only possible with Pawns. Yes, indeed, Pawns transform, but to do this they need to reach the last line. But get acquainted with the game on the chessboard, in which a piece changes after making a move. It's called "chess transformers".
Basic rules of the game of chess turners The formation of troops is normal. And they make the first move as always. But only the first one! There are “magic” verticals on the board. There are six of them. The verticals “a” and “h” are the verticals of the ROCK. Any piece that lands on these verticals turns into a ROCK and will make its next move as a ROCK, despite the fact that it does not change its appearance. The “b” and “g” verticals on the board are the “Knight” verticals. This means that any figure on these lines shouts “Igo-go!” and walks like a HORSE, although she remains who she was. The verticals “c” and “f” turn the figure into an ELEPHANT. On the Royal verticals “d” and “e”, magical transformations do not happen to the figures. Chess traditions are to blame. There cannot be more than one KING. And new Queens do not appear on the “d” horizontal line so that the pieces do not create a pandemonium on this line. PAWNS that reach the last line become Rooks - on verticals “a” and “h”, Knights - on “b” and “g”, Bishops - on “c” and “f”. On the “d” and “e” verticals, PAWNS are transformed into any piece and, of course, into the Queen.
It’s difficult to checkmate in “transformation” games. We need to get used to the rules. Despite the fact that the black King was “checked” 4 (!) times, He is, for some reason, still alive! Rook f 8 is actually a BISHOP, Queen g 7 is a KNOWN, Bishop h 7 is a ROCK, and Knight f 6 is a BISHOP. It turns out that not a single piece attacks the Black King. Therefore, He feels calm, and can bite the Bishop-RIK h 7, since it is not protected by anyone! The game can also be called “CONFUSION”, because before you learn to play it, you and your partner will get confused and mixed up many times, but there is hope that you will still get out of it!
Chess Appearances And this game on a chessboard called Chess Appearances differs from ordinary chess in that at the beginning of the game the board is completely empty. The first move should be the Kings, and everyone places their piece on any cell. Each of the opponents has a whole chess army: from the King to the Pawns, but they are behind the board. Rules for playing chess appearers on the chessboard 1. In one move, you can either place any of your pieces, or make a move of any of the pieces that have already appeared on the board. 2. Whether pieces can appear on the board with check or checkmate, the partners agree among themselves before the game. 3. It is also necessary to resolve the issue regarding the Pawns. Where should I put them? Are you on your own lines? Probably no further than your half or allowed to appear anywhere? 4. The main thing is not to confuse “eaten” pieces with those that have not yet been played. Keep “waste” away from the table. There are a few more controversial issues in this game, but even during one game all controversial issues can be resolved.
Chess "non-disappearing" - "Swedish" chess And here is another incredible popular game on a chessboard called non-vanishing chess, which is also sometimes called Swedish chess, or simply Swedish chess. It is sad to see how some pieces, having just begun a chess battle, disappear from the board and look with envy at their colleagues who are still continuing the chess battle. And this is happening due to the fault of their commanders, that is, you. So maybe you shouldn’t punish the pieces like that, but leave them in the game? Let them fight as much as they want. The only punishment, albeit a small one for them, is to hide the “beaten” pieces in the most inconvenient places so that it will take them longer to get out of there. So in this game you can safely sacrifice even QUEENS - they still won’t disappear anywhere.
Tips for playing Swedish chess Get one piece of advice. Try to hide everything that you eat from the enemy - seal it as far away as possible. The most “convenient” place for PAWNS is the side verticals. “Hide” the beaten enemy pieces either in the very corner or in their original places and let them come out again. Try to bring disorder and chaos into the ranks of the enemy army. The worse it is for him, the better for you! Black's last move: 1. . Qd 8: d 2+ (Black ate the d 2 pawn and sent it to h 4). White responds: 2. Bc1: d 2 (and sends the black Queen back to d 8). 2. . Qd 8: d 2+ (the restless Queen comes forward again and hides the white Bishop on b 1 - now White has two light-squared Bishops. So we need to hide the black Queen away so that he can no longer harm White. But where?! Like this game "NON-VANISHING WASTERS"... Let's “damage” a friend a little!
Chess players in the category love to play “SWEDES-PASSERS”. To do this, take two chessboards, two sets of chess pieces and, naturally, take two players on each side. Each team plays with black and white pieces simultaneously. Everything that a partner eats from his opponent is immediately TRANSFERRED to his teammate and he, if desired, can use these pieces. In one move, you can either move any piece or place any of the transferred pieces on the board. The first team to checkmate the opponent's King on either of the two boards wins. Rules of playing Swedish chess The rules of playing "SWEDISH" are very different. Before the game, partners must come to an agreement. Basically, restrictions are imposed on where to place the TRANSFERED pieces. For example, some play “SWEDES”, where you cannot place pieces with CHECK or MATE. Others place their pieces on any field! Pawns cannot be placed further than the 6th (3rd) horizon. Questions also arise about the promotion of a PAWN. It is clear that on the board where the PAWN has been promoted, it is a QUEEN. But who will he be if the pawn-queen is eaten and handed over to his partner? It is probably more correct to consider her a PAWN. Still, your opponent on the other board did not move it into a QUEEN!
Chess with a cube Once upon a time, in order to determine which piece should go, they threw DICE - an ordinary children's CUBE, on the sides of which POINTS are drawn - numbers from 1 to 6. Perhaps this made the game easier. You don’t need to think too much: lie down, eat pies, throw the dice, and rearrange the figures that “fell out on the dice.” Rules for playing chess with dice Each piece had its own number: KING - 1 QUEEN - 2 ROCK - 3 BISHOP - 4 KNIGHT - 5 PAWN - 6
Come on, let's play old game! Do you have a CUB? By the way, the game is quite gambling and risky. You can start any provocation without particularly fearing the consequences. Place the QUEEN or any piece for battle, eat any piece. . . , and maybe you'll get lucky. Won't fall out the right number and no one will “eat” you in return. You play with white. And you were lucky: you got 6, 2 and 4. But the enemy got only one “walking” 5 digit on the DICE, and the rest were impossible to make the first move: 3 and 4 - Bishops and Rooks locked by Pawns. White waits for a 2 or 4 to appear on the die, then they checkmate in one move: 1. F, C: f 7 X. Black dreams of getting 5 again and then the knight will jump 1. . Kf 6: h 5. Or two 6s will do. Then 1. . g 7–g 6 2. . g 6: h 5. The one who takes risks wins! And who's lucky!
Chess game "Let's all move" Rules of the game "Let's all move" Each piece and pawn of the same color can make one move. It is allowed, if a piece does not want, not to make a move with it in the “general move”. The sequence of moves of the pieces in the GENERAL MOVE depends on the general of the army, that is, on you. White made his first SUPER move. 1. a 2–a 4, b 2–b 4, c 2–c 4, d 2–d 4, e 2–e 4, La 1–a 3, Kb 1–c 3, Cc 1–g 5, Qd 1–d 3, g 2–g 3, h 2–h 4, Cf 1–g 2, Kg 1–f 3, 0–0. Note that the Figures allowed the Pawns to make the first moves in order to then make themselves more comfortable settle down. Only the f2 pawn was offended, since the Knight that had jumped out earlier blocked its path. Black's turn to dance: 1. . a 7–a 5, b 7–b 6, c 7–c 6, d 7–d 5, e 7–e 6, h 7–h 6, Kb 8–c 6, Kg 8–f 6, Cc 8 –b 7, Сf 8–e 7, Фd 8–c 7, 0–0, Аa 8–c 8.
