1. Dominoes
Six dominoes put into the square. Digits outside the square show the quantity of dots, visible in corresponding row (or column). Move one domino so that all this digits will be equal. Answer's format: Write row by row final position using X for empty cells. For example the answer will be X23,032,5XX.
Score: 5 points. | |

2. Striped snake
The snake consists of neighbouring cells of two alternating colours (black and green). Snake can not touch itself, not even diagonally. Head and tail (black cells) are marked. Digits below the square show quantity of black cells in corresponding column. Digits at right - quantity of green cells on row. Answer's format: Write the filling of forth column from left (from top to bottom). Using 1 for snake's cell and 0 for empty cell. For example the answer will be 010010.
Score: 6 points. | |

3. Queens
Place some chess queens on the board so that digits show quantity of queens that can beat this cell. Queens can not be in the cells with digits. Answer's format: Write the coordinates of all queens. For example the answer will be b1,b3,c1,e2,e5
Score: 7 points. | |

4. Japanese battleships
Place the set of battleships-5 (1 five-tube, 2 four-tube, 3 three-tube, 4 two-tube and 5 one-tube ships) in the grid. Ships cannot touch it other, not even diagonally. Digits above and at left show (in order) the size of blocks of "see" cells in corresponding row. Answer's format:Write the coordinates of all one-tube ships. For example the answer will be A3, E6, F2.
Score: 7 points. | |

5. Easy as dominoes
Two set of mini-dominoes (from 1 to five) without doubles put without intersection into the square following grid lines so that every row and column contain all digits exactly ones. Some cells are empty. Digits outside the grid show the digits you came across first from this direction. Find place for all dominoes. One of them has already shown. Answer's format: Write the dominoes which lie on marked diagonal (from top left to bottom right corner). For example the answer will be (1-2),(3-1),(1-2).
Score: 9 points. | |

6. Hexagonal route
Hexagonal field contains closed loop. Every cell of loop has exactly two neighboring cells. Loop passes through all cells with digit, every digit show the distance from this digit to the next clockwise. Answer's format: Write the order of digits along the route starting from 1. For example the answer will be 1633223.
Score: 6 points. | |

7. Map
Divide the square island to the six countries following grid lines. Every country must have connected territory and at least one cell on the square board. One cell (capital) for every country marked by letter. Digits outside the grid show the quantity of cells occupied by country, which adjoins to the boarder of square in this place. Answer's format: Write the letter corresponding to country for cell on marked diagonal (from top left to bottom right corner). For example the answer will be ADAACC.
Score: 7 points. | |

8. Arrows
Rotating clockwise the block from 7 neighboring cells in one turn, arrange the arrows so that they show in one direction. Answer's format: Write your turn using letter for central cell. For example the answer will be ABB.
Score: 6 points plus 2 points for shortest solution. | |

9. Multiplied skyscrapers
Buildings with height from 1 to 7 floors are in every cell of square. All building in every row or column have different height. Numbers outside the grid show the product of number of floors in the visible buildings. Fill the square. Answer's format: Write the number from marked diagonal (from top left to bottom right corner). For example the answer will be 1123
Score: 7 points. | |

10. Battleships observers
Place the set of battleships (tubes must be on the gridlines intersection, and ships must follow lines) so that quantity of tubes visible by three observers will be minimal. Ships cannot intersect each other. Ships cannot be in point with observer. In example the observer X sees 3 tubes. Answer's format: First write the numbers of visible tubes, then write coordinate of all tubes. For example the answer will be 19,a5,b5,c2,c5,d1,d3,d5,e3,e4,e5
Score: 40 minuses quantity of visible tubes. | |

11. Numberp
Using digits 1,2,3,4,5,6,7,8,9,0 exactly ones, arithmetic signs +, - , x, / exactly ones and any number of brackets write the arithmetic expression which is closest approximation for number p = 3,1415926535897932384626433832795... Digits and signs can follow in any order. Example: (1 - 23 + 45 x 67) / 890 = 3.3629…
Difference is equal 0.2213... Answer's format: Write your expression. For example the answer will be (1-23+45*67)/890
Score: 2 points for every 0 in difference minus one fifths of first significant digit in difference. For example the score will be 2x1 - 2/5 = 1.6 points. | |

12. Unique route
Paint some cells in the square 10x10. Then choose the start and the finish cells so that route passes through all white cell will be unique. Route must pass through all white cell one time and can go from one cell to other through cell sides (not corners). Try to minimize the number of painting cells. Answer's format:First write the number of painted cell, then coordinates of start and finish cell and last the coordinates of all painted cells. For example the answer will be 15: D7,E8;A4,A7,C1,C3,C7,C10,E9,G1,G4,G6,G8,G10,I5,J3,J8.
Score: 25 minuses 2 points for every painted cell. |