Czech federation of mancala games

Master of logic games 2012 - part Toguz Kumalak, online qualificaton for 2nd World Championship in Toguz kumalak.

Rules of competition: Competitors - juniors up to 18 years with full amount of points can attend Junior World Championship. Other competitors juniors will be invited based on number of points achieved and capacity of playing hall.

Toguz kumalak (9 balls) is a game for two players. A board with two rows of nine cups and nine balls in each cup at the beginning is used for this game. But we start at smaller board, with 5 cups in each row and 5 balls in each cup.

Initial position is like on this picture

H5H4H3H2H1
D1D2D3D4D5

You have always the bottom row.

Choose any cup on your side, take everything into your hand, go along in anti-clockwise direction and put one ball into each cup. Put first ball into cup you have chosen (and which is empty now…). Situation on the board, when you start in D3 is on the following picture.

H5H4H3H2H1
D1D2D3D4D5
H5H4H3H2H1
D1D2D3D4D5

Where did you drop the last ball? Into cup H2. It is on the opponent side and now, there is an even number of balls. This means, that you can capture the balls from H2 and move them to your long storage cup. See, how is the situation on the board after capture on the following picture.

H5H4H3H2H1
D1D2D3D4D5

Now the opponent plays. The game is finished, when one of the players has 26 or more balls in his storage cup. He is the winner. The game can end even sooner, if a player on the move has nothing in his cups. Then the opponent moves everything from his cups to his storage cup, and both calculate the score of the game.

H5H4H3H2H1
D1D2D3D4D5

You can play even one ball cups and even capture balls. See the picture. Bottom player can play D5 to H1 and capture two balls in H1. But he can of course escape with D1 to D2, to prevent opponent’s move H5 to D1 and capturing two balls.

First example problem: It is your turn, you will play D4, where you have eight balls. Where do you put the last ball?

Second example problem: Where do you put the last ball, if you play D3 with 16 balls in it?

Third example problem: What will happen, if you put last ball into your cup?

Solution: 1. D1, 2. H3, 3. You do not capture anything and your opponent is on the move.

First problem: (1 point)  You play D2. How many balls will be at the end of your move in H4? (if you capture, it means after moving balls to storage cup)

0 1 5 6 7

H5H4H3H2H1
D1D2D3D4D5

Second problem: (1 point)  You play D5. How many balls will be at the end of your move in H1? (if you capture, it means after moving balls to storage cup)

0 1 4 5 6

H5H4H3H2H1
D1D2D3D4D5

Third problem: (1 point)  It is your turn and you want to capture as many balls as possible in your move. Which cup you choose?

D1 D2 D3 D4 D5

H5H4H3H2H1
D1D2D3D4D5

Fourth problem: (1 point)  It is your turn and you want to capture as many balls as possible in your move. Which cup you choose?

D1 D2 D3 D4 D5

H5H4H3H2H1
D1D2D3D4D5

In many games is important to be able to imagine, how will the board looks like after few moves. Next problems contains initial situation and sequence of moves. You should write number of balls in selected cup or number of captured balls.

Fifth problem: (2 points) Sequence of moves: 1. D5, 2. H4. How many balls will be at the end of you move in D2? (if you capture, it means after moving balls to storage cup)

0 1 6 7 8

H5H4H3H2H1
D1D2D3D4D5

Sixth problem: (2 points) Sequence of moves: 1. D3, 2. H3. How many balls will your opponent capture during playing this sequence from D3?

0 1 2 5 6

H5H4H3H2H1
D1D2D3D4D5

Seventh problem: (3 points) Sequence of moves: 1. D3, 2. H4, 3. D5, 4. H5. How many balls will both players capture together during playing this sequence?

0 2 4 6 8

H5H4H3H2H1
D1D2D3D4D5

Now we switch to bigger board, (2x9 cups) and we will explain the rule of Tuzdek.

All previously mentioned rules are valid. And the following:

If you put last ball into cup on opponent side and in that cup are now exactly 3 balls, you create Tuzdek (trap). Each player can create just one Tuzdek during a game. It is not possible to delete it or move it to other place - it is on the same place till the end of the game. You cannot create Tuzdek in last cups (D9 a H9). You cannot create second Tuzdek in the cup with the same number as first Tuzdek (e.g. First Tuzdek is in H6, second cannot be in D6).

What is good on Tuzdek? Everything, what falls into Tuzdek is immediately moved to your storage cup!!! The 3 balls, which let you create Tuzdek go to storage cup as well.

On the following picture, there is bottom player on the move. He can create Tuzdek in cup H2 if he plays cup D8. Player will move three balls from H2 to storage cup and put the red ball into H2 (to show that there is Tuzdek).

H9H8H7H6H5H4H3H2H1
D1D2D3D4D5D6D7D8D9
H9H8H7H6H5H4H3H2H1
D1D2D3D4D5D6D7D8D9

Fourth example problem: If the bottom player plays D8 and his opponent H9, will be Tuzdek created in D9?

Fifth example problem: If the bottom player plays D8 and his opponent H8, will be Tuzdek created in D2?

Solution: 4. NO - last cup, 5. NO - cup with same number

Eighth problem: (2 points)  How many balls will both players get together into storage cups, if bottom player plays D6?

0 2 4 6 8

H9H8H7H6H5H4H3H2H1
D1D2D3D4D5D6D7D8D9

Nineth problem: (3 points)  Both storage cups contains 79 balls. Bottom player is on the move. Who is the winner and what is the score of the game? (You are bottom player and you want to win as many balls as possible)

Draw 81:81 Bottom wins 82:80 Opponents wins 82:80 Bottom wins 83:79 Opponents wins 83:79

H9H8H7H6H5H4H3H2H1
D1D2D3D4D5D6D7D8D9

Tenth problem: (3 points)  Both storage cups contains 79 balls. Bottom player is on the move. Who is the winner and what is the score of the game?

Draw 81:81 Bottom wins 82:80 Opponent wins 82:80 Bottom wins 83:79 Opponent wins 83:79

H9H8H7H6H5H4H3H2H1
D1D2D3D4D5D6D7D8D9

Eleventh problem: (4 points)  How many moves can both players make until all their balls will end up on the other side or in Tuzdek/storage cup?

Opponent 2 3 4 5 6 7 8
Bottom player 2 3 4 5 6 7 8

H9H8H7H6H5H4H3H2H1
D1D2D3D4D5D6D7D8D9

That is everything.

Now, please, fill in some information about you:

First name and surname
School - street, town
School class (how many years you attend school)age 11 and youngerage 12 to 15age over 15adult
Email (whom can we write, if you win)
Send me info, when new competition will be available
country
(I agree that all info can be stored and that my name, town and country will be show in list of solvers and winners. I agree with the rules of competition.)