1. Twenty two matches
I have made a 4-digit number with 22 matches with the digit forms shown on the top. Then, having shifted some matches, I could write the same number in Roman numerals shown on the bottom. Find the initial number. Format of the answer: Write the initial 4-digit number.
Score: 5 points. | |

2. Tent pairs
There are some trees on the grid. Locate two tents near to each tree so that they touch the tree on the edge or at the corner. Tents on the grid can not touch each other, not even diagonally. The numbers on the sides reveal the number of tents on the respecting row or column. | |

Example: | |

Format of the answer: Write the arrangement of the tents on the marked diagonal, from top-left corner to bottom-right. Use "1" for tent and "0" for an empty cell. For the example the answer would be 000001.
Score: 6 points. | |

3. Poly-polygonal figures
Cut a square along the grid lines into some polygonal figures, having different quantity of corners. The numbers at the left and on top reveal the number of polygonal figures seen on the given row or column. Numbers at the right and on bottom reveal the total quantity of corners in the polygonal figures seen on the given row or column. | |

Example: | |

Format of the answer: Mark all the cells with the number of corners of the figure it belongs to. Then write the numbers on the shown diagonal from top-left to bottom-right. For the example the answer would be 8, 8, 12, 12, 4.
Score: 7 points. | |

4. "Prime" grid
Completely fill the 10x10 grid with snakes of different lengths. Lengths of all snakes are prime numbers. A snake consists of neighbouring cells and has a head and a tail. A snake can not touch itself, not even diagonally. The numbers on the sides show the number of cells on the given row or column occupied by the same snake that is seen first from that direction. | |

Example: | |

Format of the answer:Mark the cells of a snake with the number equal to its length. Then write the numbers on the shown diagonal from bottom-left to top-right. For the example the answer would be 11, 7, 13, 7, 13, 11.
Score: 7 points. | |

5. Weather vanes confusion
On the grid of 5x5, 25 weather vanes are seen. On the edges of the grid, giant platforms are placed which create winds blowing with equal force in one of the 8 directions. These directions are designated as: N - North, E - East, S - South, W - West. Intermediates - by the appropriate combinations of the letters. A weather vane turns to the side where the strongest wind comes from. The force of that or other wind is determined by the sum of the letters. In the example, there are five winds coming to the cell at the top of "4": SE + S + SW + W + N. That are three Ss, two Ws, one E and one N. Therefore the strongest wind is S, which is already written on that cell. But, some weather vanes stay in complete confusion, as can not define where to turn. In these cases total number of the strongest winds is written. In the example, there are four winds coming to the vane at the bottom-right corner: S + W + N + E. All of them of equal force, therefore the number "4" is written on it. Find where every giant platform blows to. | |

Example: | |

Format of the answer: By beginning with the marked square, list directions of all winds, moving clockwise. For the example the answer would be: SE-SE-SE-S-SW-SW-W-W-N-NW-N-N-E-NE-NE-E.
Score: 8 points. | |

6. Equation from domino
From a standard set of dominoes 0:0 is deleted and 5 non-standard dominoes (2:8, 3:7, 4:7, 5:7, 6:8) are added, for a total of 32. Locate all dominoes in the grid below so that in all 6 rows and 6 columns the equalities become true. All signs are already placed. The numbers can not begin with zero. You can turn the dominoes. The locations of the 5 non-standard dominoes are marked red. | |

Format of the answer: Write the numbers on the red cells from top to bottom. Order the numbers on the same row from left to right.
Score: 9 points. | |

7. First passers. The twins in quarrel.
Locate the letters A, B, C, D, E, F in the grid so that in everyone row, every column and on two diagonals each letter is seen exactly once. Thus, one cell in every direction will be empty. The identical letters and empty cells can not touch each other not even at corners. The letters on the sides of the grid reveal the first letter seen from that direction. | |

Example: | |

Format of the answer: Write the contents of the third column from top to bottom, using "_" for the empty cell. For the example the answer would be C_BDA.
Score: 8 points. | |

8. Serial numbers
The numbers give 8 pairs of words. Each number corresponds to a unique letter. The words in each pair are incorporated by the same principle. By understanding what they consist, find the number-letter key. Example: Format of the answer: Write the letters in ascending order of the numbers appropriate to them. For the example the answer would be CESONDTURY.
Score: 6 points. | |

9. Magic sums
Make a magic square of 9x9. In each row, each column and on two main-diagonals there are all digits from 1 to 9. Numbers on the sides of the grid are equal to the sum of the first three digits in that direction. | |

Example: | |

Format of the answer: Write the digits on the second column from top to bottom. For the example the answer would be 321678594.
Score: 9 points. | |

10. Division by arrows
A clock has three arrows (hands). Second arrow turns by an interval of 1 second. After its each turn, minute and hour arrows turn for the appropriate angle. Assume that all arrows have lengths equal to the radius of the clock-circle and identical thickness. What time will it be on the clock, when the circle will be divided by arrows into three areas having angles as close to each other as possible? Minimise the sum of the individual differences of the angles from 120 degrees. | |

Example: | In this case the clock shows 10:15:00. Angles are: 90, 217.5 and 52.5 degrees. Therefore the some of the differences is [120-90] + [217.5-120] + [120-52.5] = 195. |

Format of the answer: HH:MM:SS.
Score: 18/(sum of the differences). | |

11. Battleships - chess
On a chess board you have to locate chess pieces so that a full standard fleet of 10 ships can be placed into the non-attacked cells. The ships can not touch each other, not even diagonally. All other cells (other than the ones that pieces are on) of the board must be attacked at least by one chess piece. The chess pieces can not attack each other. You have unlimited quantity of knights (N), bishops (B), rooks (R), queens (Q) and kings (K). Find a board with a) minimum b) maximum quantity of chess pieces. | |

Example for a board of 7x7 with a mini-fleet: | Standard fleet: |

Format of the answer: For each requirement (a and b), write the coordinates of all the chess pieces in your solution. For the example on a 7x7 board with a mini-fleet the answer would be: Bg7, Rb6, Rd2, Kf1, Kf4.
Score: a) 2 points for 6 chess pieces and 2 extra points for each piece less.b) 1 point for 9 chess pieces and 1.5 extra points for each piece more. | |

12. Pentasieve
Place a standard complete set of 12 pentominoes in a rectangular area of any size so that there is a maximum quantity of empty individual cells. But, cells can not touch each other, not even diagonally. You can rotate and reflect the pentominos. | |

Example: | |

Format of the answer:Write the contents of the rectangle row by row using the pentomino letters for occupied cells and dots for empty cells. For the example the answer would be:
.XFFLLLLV,XXXFFUULV,IXZF.UVVV,ITZZZUUPP,ITTTZ.WPP,ITYNNNWWP,IYYYYNNWW Score: 2 points for every empty cell over 12. |