Rambler's Top100
4-th round puzzles will sent at 03 December
Print version4-rd round puzzles
Author - Vladimir Portugalov

1. Special cross-sums
Here are 6 mini-puzzles. In every puzzle you must fill cells with different digits from 0 to 9, so that numbers at top and at right show the sum of digits in corresponding column or row. It is not necessary to use all ten digits in every puzzle. The digits in the cells with same letter must be equal.
Illustration for puzzle 1
Answer's format: write digits, which occupy cells with letters, in increasing order. For example the answer will be: 127.
Score: 8 points.

2. Blot
Cut the given figure by grid lines onto 10 pieces with same shape and size. Pieces may be rotated and reflected.
Illustration for puzzle 2
Answer's format: write the belonging of cells of marked row. Number the pieces from left to right. For example the answer will be: 111234567.
Score: 5 points.

3. City wall
Draw the city wall - closed continuous loop one cell width, which cannot intersect or touch itself. Letters 'O' denote the guards. There must be exactly one guard on the wall at every row and column.
Illustration for puzzle 3
Answer's format: write the columns with wall guards for every row from top to bottom. For example the answer will be: bdafce.
Score: 6 points.

4. Bands
Divide the square by grid lines into the bands with one cell width and different length. Cell with digits must belong to band of corresponding length. Every band must have at least one digit inside.
Illustration for puzzle 4
Answer's format:write the digits for diagonal cell from left-bottom corner to right-up corner. For example the answer will be: 322424.
Score: 6 points.

5. Boarding
Place two fleets (trade and pirate's) at the battle field. Every fleet has one four-tubes ships, two three-tubes, three two-tubes and four one-tubes. All ships cannot touch the other ship of the same fleet. Every pirates' ship boards (touch by exactly one cell) one trade ship having same size. Pirates' ships can also touch other trade ships, but without battle.
Crosses mark the cells of trade ships which boarding by pirates. Numbers at the bottom and rights denote overall quantity of cells occupied by ships in corresponding column or row.
Illustration for puzzle 5
Answer's format: write the content of marked diagonal from left-bottom corner to right-up corner. Use 'X' for blank cells. For ships use digits (denotes the ship size) with letters (T for trade and P for pirates'). For example the answer will be: X, X, 2P, X, 1P, 2, X.
Score: 7 points.

6. Multiplication
In multiplication problem some segments of digits are omitted. Restore all digits.
Illustration for puzzle 6

Answer's format: give the product value. For example the answer will be: 224.
Score: 9 points.

7. Movement
5 robots move along the simple closed loop going throw all cells in square. At the three pictures you can see positions of robots with interval of 5 steps (robots moves at neighbour cell during one step). Define the robots' path.
Illustration for puzzle 7
Answer's format: write the positions of robots after next five moves. For example the answer will be: 2, d4.
Score: 7 points.

8. Alphabet placing
You must place Latin letter into four grids without rotating. Each grid must contain six letters (two letters will be superfluous). Letters cannot intersect or touch each other. Digits outside the grids show the quantity of letters' elements which intersect the central line of corresponding row or column. Some elements are already placed. Letters' shapes are given.
Illustration for puzzle 8

Answer's format: write 2 superfluous letters. For example the answer will be: 25.
Score: 10 points.

9. Pentamino in half
Complete set of pentamino devided into two groups of six elements was put into two grids 99 so that elements cannot touch or overlap each other. Pentamino can be rotated and mirrored.
Find the position of pentamino if the numbers outside the grid show the sum of distances from grid border to nearest element for both grids.
Illustration for puzzle 9
Answer's format: write the elements which occupy the same grid as element I. For example the answer will be: PY.
Score: 8 points.

10. Same results
First replace some digits with arithmetical operation signs (+, -, /, ). Then cut off any quantity of strips (one cell width), containing correct arithmetical expression (with at least one arithmetical sign) which reading from left to right or from top to bottom. Neighboring digits (horizontally or vertically) can form the multi-digits numbers. All expression must be different (including the permutation of items and multipliers). Try to obtain maximum number of expression with equal value (negative or non whole value are possible). Operation priority is standard (first and /, then + and -).
Illustration for puzzle 10
Answer's format: first write the expressions' value. Then write all signs and its positions. Separate by commas signs used in different expressions. For example the answer will be: 5: +a2, *c2, -b4, -e2+e4, /c5.
Score: 2 points for every expression over 5.

11. Prime numbers
Choose any 4 numbers so that putting them (in different order) into the expression
Illustration for puzzle 11
gives you maximum quantity of different prime numbers.

Example: for numbers 1,2,3,4 we obtain 3 prime numbers:
Illustration for puzzle 11
Answer's format: write the numbers which you have chosen. For example the answer will be: 1,2,3,4.
Score: 1.5 points for every prime number over then 3.

12. Rally - freestyle
Starting with cell marked "S", it need go to the finish ("F") with minimum moves. During moving you must go throw all "check-points" (dark cells with digits), in increasing order (additional passing out of order is possible).
Speed is the quantity of cells, which you go at one move in one direction. You can choose start speed from 1 to 4 in any direction. I.e. after first move you can occupy any blue cell. Then if you do not change the direction then your speed increases by 1 cell per second. If you turn by 60 degrees - your speed stays the same. If you make 120-degrees turn then your speed decreases by 1 cell per second.
All "check-points" and finish you can pass at any speed. But you cannot go out the field during the race.
Illustration for puzzle 12

Illustration for puzzle 12

Answer's format:first write starting speed. Then specify the direction for every move. For example the answer will be: 2, 43113342.
Score: 45 minus rase time.