1. Clouds
Put eight clouds (rectangles with size 2õN, N is natural number grater then one) into the diagram. Clouds cannot touch each other, not even diagonally. Numbers outside the grid show the quantity of cells occupied by clouds in corresponding row or column. Answer's format: write the filling of diagonal cells (from left top corner to right bottom). Use 1 for cloud's cell and 0 for empty cell. For example the answer will be: 11011.
Score: 6 points. | |

2. Magnets without borders
Cut the given strips into rectangles 1õ2. Some of the rectangles is magnet (with "+" and "-" signs) and other id the neutral. Cells with same sign cannot touch each other by side. Numbers outside the grid show quantity of signs "+" and "-" clouds in corresponding row or column. One cell is already given as neutral. Answer's format: give the content of diagonal from left top corner to right bottom. Use 0 for neutral cell. For example the answer will be: ++0+.
Score: 8 points. | |

3. Pyramid
Pyramid consists from beads and rods. One bead may be connected with beads of same or neighbour layers. Rods cannot intersect. Numbers in the beads show the quantity of rods going from this bead. The sum of numbers in beads of first (A, B, C) and second (D, E, F) layers is equal to 19. The sum of numbers in beads of second and third (G, H, I) layers is equal to 15. The sum of numbers in beads of third and forth (J) layers is equal to 11. Determine all rods. Answer's format: write the digits for beads A,B,C,D,E,F,G,H,I,J on order. For example the answer will be: 2151331.
Score: 6 points. | |

4. Russian battleship
Place the complete set of battleship into the grid. Ships cannot touch each other not even diagonally. The numbers show the distance (horizontally or vertically) from the center of numbered cell to the center of ship's cell. And there is exactly one ship's cell at this distance for every number. Ships cannot occupy numbered cell. Ship's cell may be not pointed be number or pointed by more then one number. Answer's format:write the coordinate of one-tube ships. For example the answer will be: a6,c4,f1.
Score: 7 points. | |

5. Patience
Place cards from 2 to 10 of four suits (one card is superfluous) into the grid. Cards having common point (may be only corner) must have different suits and number difference at least 3. Number and suits outside the grid show that only such cards may be in corresponding row or column. One suit and one value are already given. Answer's format: write cards from marked column, using such denotation: S(spades), C(clubs), D(diamonds), H(hearts). Answer my be like this: 3S, 4C, 5D, 6H, 7S, 8C.
Score: 8 points. | |

6. Dag-word
Place name of Dagestan cities into the grid and obtain the correct linked crossword. Words can read in any four directions (from left to right, from right to left, from top to bottom and from bottom to top). Any row and column contain exactly two equal letters. Numbers outside the grid show the quantity of occupied cells in corresponding row or column. Answer's format: write the content of marked column from top to bottom, using "-" for empty cell. Answer may be like this: A-BC-DEF--
Score: 8 points. | |

7. Arrows
Put arrows into empty cells. Arrows in outer cells must show inward the square 9õ9. Arrows in inside cells can show or inward square 3õ3 or outward. Numbers in the cells show the quantity of arrows showing to the cell. Arrows cannot show to cells which separate from arrow by black square or another arrow. Black cells haven't arrows. Answer's format: write the quantity of diagonal arrows for top, right, bottom, left rows and for inner square in order. For example the answer will be: 3,3;3,2,3.
Score: 7 points. | |

8. Skyscrapers
Place buildings with height 1-7 into the grid so that every line contains only building with different height. Numbers outside the grid show the quantity of buildings visible in line from this direction. Answer's format: write numbers in the middle vertical from top to bottom. For example the answer will be: 21.
Score: 9 points. | |

9. Easy as sum
Every row and every column contain digits from 1 to 6 exactly once (one cell is empty). Numbers at top and rights show the sum of first and last digits in corresponding row or column (first from both directions). Numbers at bottom and left show the sum of second and fifth digits (second from both directions). Place the digits. Answer's format: write digits in marked diagonal from top left to right bottom corner. For example the answer will be: -233-.
Score: 9 points. | |

10. Pentis
Pentaminoes of two shape: Y and X fall in order (first Y, then X, then Y again and so on) into the grid 8x16. You can rotate and reflect pentaminoes. Obtain maximum numbers of completely filled horizontal lines in the grid. Elements cannot jut out the grid. In the grid elements can move only vertically. Answer's format: first write the number of completely filled lines, then for every element give vertical (letter) containing cell with dot. For Y element give the orientation using the giving denotations. For example the answer will be: 4: e8,b,g3,d,a4,c,f3,b,e5.
Score: 1 point for every completely filling line. | |

11. Labyrinth
Choose any cell in first column for start and pass through labyrinth to the last column. Number of visited cells in every column must be no more then number at the top of the column. Every cell must be visited only once. Obtain path with maximum length. Answer's format: first write path's length, then for every column from left to right write letters for visited cells.. Answer must be like this: 55: g, fg, fij, fghi ….
Score: 0,8 for every visited cell over then 66. | |

12. Optimum dominoes
Put all elements from complete sets into the grid. Elements must form simple closed loop which cannot touch itself even diagonally. Path cannot contain squares 2õ2. Numbers on the halves with common side must be equal. Maximize the sum of numbers which you read in horizontal lines. Answer's format: first write the sum, then give the filling of grid row by row, using "-" for empty cell. For example the answer will be: 43113: ---,22000,2---0,21111,---.
Score: best result - 11 points, and 0.5 point les for every next. |