Download 5. Every second. Place 12 different pentamino elements (may be

13 –th RUSSIAN PUZZLE CHAMPIONSHIP
ONLINE COMPETITION - INSTRUCTIONS
2010, June, 5st, 9-11.30 GMT
Three part of the competition will be provided all together for 150 minutes. Be careful – contest file
will contain only grids, not instructions and examples. Answers should be submitted at the contest
page: http://diogen.h1.ru/cgi-bin/contest/contest.pl?id=36
For any question write to forum: http://www.forsmarts.com/forum/index.php
PART 1. MIX
1. Stripes. Put numbers from 1 to 13 to the circles and divide the grid into stripes. Stripes have one cell width
and different lengths of 1, 2, …, 13 cells. Ends of each stripe have circles with corresponding number. Stripe
of length 1 has only one circle. Stripe cannot touch itself.
12 5
10
1
13
12 5
4
13
10
3
3
8
7
4
10 3
5
12
6
8
9
7 11
9
6
4
8 13 6 11
2
2
9
7 11
2
Answer key: write the numbers written into the empty circles going row by row from left to right. For the given
example the answer would be: 1, 7, 3, 8, 10, 5, 12, 9, 4, 13, 6, 11, 2.
2. Trapeziums. Place some trapeziums into the grid. Each trapezium consists of one cell and half.
Trapeziums cannot touch each other even by a corner. Numbers outside the grid show the number of triangles
of given form in corresponding row or column.
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Answer key: write the content of two main diagonals: first from bottom left to top right, then from top left to
bottom right. Use E for empty cell, F for fully occupied cell and H for partially occupied. For the given example
the answer would be: HEFHEHEF,HEEFEFEH.
3. Battleships. Place standard battleships fleet (one 4-cells, two 3-cells, three 2-cells and four 1-cells ships)
into the grid. Ships cannot touch each other even diagonally. Numbers in the grid show the numbers of
unoccupied cells visible from the cell in four possible directions (horizontally or vertically). Ships cannot be in
the cells with number.
6
1
2
5
8
10
5
6
3
2
5
6
2
5
3
6
2
1
8
10
5
6
3
2
5
3
6
2
Answer key: write the numbers of ships lying horizontally for each size (2-cells, 3-cells, 4-cells) in order. For
the given example the answer would be: 1, 0, 0.
4. Areas. Divide the grid into areas which consist of 1, 2, 3, 4, … (each value is used exactly once) triangular
cells. Numbers outside show all values which are in the corresponding directions.
45
45
2567
47
2567
47
5 5 5
7 7 7 2 2 5 5
257
257
3 3 6 7 7 7 4 4
3 6 6 6 7 4 4
37
1 6 6
37
16
16
Answer key: write the content of bottom row. For the given example the answer would be: 1 6 6.
5. Every second. Place 12 different pentamino elements (may be rotated or mirrored) into the grid. Element
cannot touch each other even diagonally. From the left to the right, next from above to the bottom of the grid
every second cell, occupied by pentamino (1-st, 3-rd, 5-th, …) are visible.
I
L
Y
N
P
V
F
T
Z
X
W
C
Answer key: write the names of elements touching the border going clockwise starting from top left corner.
For the given example the answer would be: V, X, X, W, P, L, C, C, F, F, T, Z.
6. ХО-chain. Sixteen 2х2 square form a chain. Fill in the squares with X and O signs. All squares should be
different - all possible variations of X and O are used (the complete set is given inside the chain). Neighbor
squares should differ at exactly one sign. Some signs are already placed.
X
O
X
O
X
X
X
X
X
X
X
X
X
X
O
O
X
O O
X
X
O
X
O
X
O
X
X
X
X
O
O
X
O O
O
O
X
O
X
O
X
O
X
X
X
O
O
X
O O
X
O O
O O
O O
O O
X
X
O
O O
X
O
X
X
O
O
X
O O O O O
O
O
X
O
X
O
X
X
X
X
X
X
X
X
X
X
X
O
O
X
O O
X
X
X
X
X
X
O O O O O O
X
X
X
X
O
X
O
X
O
X
X
X
X
O
O
X
O O
X
X
X
X
X
O
X
O
X
O
X
O
X
X
X
O
O
X
O O
X
X
X
X
O
O
X
X
X
O
X
O
O
X
X
O
X
O
O O
O
X
X
X
X
X
X
O
O O
O O
O O
O O
X
X
O
O
O O
O
X
O O O O
X
O O
X
O
O
X
X
X
O
X
Answer key: write the content of top row, followed by the content of bottom row. For the given example the
answer would be: OXOOOOOXXX, OXOOXOXOXO.
7. Arithmetic operation. Put digits form1 to 9 into the circles (each digit is used exactly once) and rectangles
with arithmetic operation between the circles. Each digit should be result of corresponding operations applied
to the left and top digits.
+
7
+
3
5
3
x
2
/
6
+
1
+
2
-
4
-
8
x
3
x
5
7
-
3
4
+
1
4
-
+
x
5
3
2
2
x
6
3
+
2
8
+
/
-
7
6
3
9
-
1
8
x
5
5
Answer key: write the digits at the circles row by from left to right. For the given example the answer would
be: 734,268,915.
8. Domino. Place one black domino into each of outlined area. Each row and column should have exactly four
black cells. Dominoes cannot touch each other even diagonally.
Answer key: write the number of cells occupied by dominoes in the two main diagonals (first from top left to
bottom right, then from top right to bottom left). For the given example the answer would be: 2, 2.
9. ZLOTI-tetramino. Divide the grid into tetraminoes. Each tetramino should contain one letter which gives
tetramino name.
T
T
I
L
Z
Z
O
T
O
Z
L
Z
O
T
Z
O
T
Z
L
O
Z
I
I
Answer key: Write the number of vertical T-elements (the straight line through 3 neighboring cells of element
is vertical). For the given example the answer would be: 1.
10. 1, 2, 3 and black circle. Put different tetramino elements into the grid. Elements cannot touch each other
even diagonally. Each element should contain one black circle. Fill in other cells of tetramino with digits 1, 2, 3.
Numbers outside the grid show the sum of digits in the corresponding row or column.
4
1
6
2
4
3
1
2
6
2
1
6
6
3
3
3
6
2
6
1
1
5
3
6
2
3
1
6
3
3
3
2
6
6
3
2
3
3
1
6
5
3
6
Answer key: write the number of horizontal and vertical (32) (not (23)!) combinations in the elements . For the
given example the answer would be: 2, 1.
11. Pentatouch. Place complete pentamino set into the grid. Elements cannot touch each other even
diagonally. The could be rotated and/or reflected. All empty cells which touch (by a side) to exactly two
elements are marked with circle. Some circles contain letter which show the touching elements..
I
L
Y
N
P
WP
WP
FZ
FZ
V
F
T
CI
CI
Z
LN
X
W
LN
XT
XT
C
VY
VY
Answer key: write the content of main diagonals (from top left and then from top right). Use letter of
pentamino for occupied cells and E for empty cells. For the given example the answer would be:
EFEEEEELLEEN, EEECEEEEEETT.
12. Loop. Draw single closed loop which cannot touch itself even diagonally. Every third corner of the loop is
marked by a circle and number of cells of the loop visible from the corner is written to the circle.
5
5
6
6
8
3
8
3
3
3
3
3
2
2
8
8
Answer key: write the length of all horizontal; segments of the loop which have no marked ends row by row
from left to right. For the given example the answer would be: 2, 1, 3, 1.
13. From 1 to 10. Put the numbers from 1 to 10 into the grid. The cells with number can not touch each other
even diagonally. The given numbers show the sum in the neighboring cells, as in the minesweeper.
5
8
3
13 15
3
7
11
5
9
8
15
8
9
12 11
10
6
8
3
3
3
5
8
2
7
9
13 15
7
11
15
1
4
9
9
12 11
10 10
1
1
Answer key: write the numbers row by row from top to bottom. For the given example the answer would be:
56, 4, 39, 82, 1, 710.
PART 2. BAKER'S DOZEN
Write the numbers from 1 to 13 (all are used once) in each of the 13 puzzle. Some of equal numbers of
different puzzles connected by gray line.
1. Honey. The numbers in neighboring cells (having common edge) must differ by at least 3 (i.e. not at 1 and
2).
11
5
1
5
8
12
2
9
1
4
13
7
12
3
6
10
Answer key: write the number of the external loop going clockwise from the top. For the given example the
answer would be: 11, 7, 3, 10, 4, 8.
2. Currents. For each black dot the sum of the numbers of incoming arrows is equal to the sum of outgoing
arrows.
1
1
11
3
7
12
10
9
13
2
5
6
8
4
Answer key: write the numbers of the external loop going clockwise from the top. For the example the answer
would be: 1, 12, 4, 2.
3. Scales. Each of the scales should be balanced.
Answer key: write the numbers in the top row from left to right. For the example the answer would be:
12, 2, 13, 8.
4. Distances. The distance between the circles should increase in order: /1,2/</2,3/</3,4/</4,5/</5,6/<…
(distance between circles X and X+1 should be bigger then distance between X and X-1)
8
13
5
11
10
4
7
12
2
6
1
3
9
Answer key: Five first numbers from left to right, from top to bottom. For the example the answer would be:
8, 13, 5, 11, 10.
5. Sums. Numbers in the circles show the sum of the three neighboring numbers.
9
15
15
11
29
20
13
15
27
23
24
29
29
5
1
20
13
13
2
27
23
6
10
24
8
4
15
29
12
23
7
23
3
Answer key: the numbers in the top row. For the example the answer would be: 11, 5, 1, 4.
6. Chess. Put the numbers in the white cells. Sums for horizontal, vertical and some diagonal rows are given.
Numbers with difference 1 should not touch by a corner.
20
21
16
12
27
8
28
20
29
17 11 32 9 22
21
16 1
7
8
12
9
3
27 5
12
10
8
2
6
28 11
13
4
17 11 32 9 22
29
Answer key: write the five top numbers. For the example the answer would be: 1, 7, 8, 9, 3.
7. Arithmetic operations. Each number is obtained from the left neighboring number with the corresponding
arithmetic operation.
x3
.+2
.+3
6
.+2
8
.+3 11
-2
x2
7
-2
5
x2
10
-1
/3
13
-1
12
/3
4
-7
-1
3
x3
9
-7
2
-1
1
Answer key: write the four left numbers. For the example the answer would be: 6, 7, 13, 3.
8. Connections. The sum of numbers in connected circles is given for each number.
1=4
2=15
3=13
4=10
5=21
6=22
7=29
8=23
9=5
10=14
11=2
12=18
13=18
8
13
3
10
7
4
2
6
12
1
11
5
9
Answer key: write the four numbers in second row. For the example the answer would be: 10, 7, 4, 2.
9. Differences. The difference or the sum between some numbers is shown.
15
3
16
3
4
20
19
6
14
6
20
8
16
9
18
13
7
9
12
15
9
3
5
20
6
19
6
8
14
6
2
7
1
8
7
10
9
11
9
18
20
14
4
14
4
Answer key: write the numbers in the middle row. For the example the answer would be: 13, 6, 8, 2, 11.
10. Expressions. Three horizontal, three vertical and two diagonal mathematical expressions are true.
/
=
+
+
+
=
-
=
-
=
=
x
10 /
=
x
x
+
+
+
13 -
x
=
5
=
=
x
x
7
=
2
x
-
x
=
+
8
+
+
9
=
1
+
=
-
=
=
=
12
4
6
3
11
Answer key: write the three numbers for the diagonal from top right to bottom left. For the given example the
answer would be: 10, 7, 8.
11. Path. Find a path going through all circles exactly once. Path can intersect itself, Write the number in the
circles in order. Path doesn’t have to make turn at the circle, but it can’t jump over the circle.
5
11
4
12
2
1
3
1
9
6
10
13
8
7
Answer key: write the three top numbers. For the example the answer would be: 5, 4, 11
12. Capsules. The numbers outside the grid show the sum of numbers in the capsules in the corresponding
row or column.
2
7
16
11
9
10
5
8
1
17
13
4
3
6
12
15
13 18
19 14
7
22 12 22
Answer key: write the four top numbers. For the example the answer would be: 2, 7, 9, 10
13. Ear. The numbers show the sums in the corresponding lines.
20
18
22
20
8
23
16
16
25
8
26
5
11
9
18
6
7
23
13
4
2
16
10
1
25
8
3
12
8
16
22
8
26
Answer key: write the numbers in the middle row. For the example the answer would be: 9, 6, 2, 4, 13.
12. Capsules
9. Differences
5. Sums
1. Honey
6. Chees
2. Courents
18
25
16
=
=
-
/
20
13. Ear
-
+
=
=
-
+
8
22
=
+
x
=
+
26
8
=
x
10. Expressions
16
23
+
x
x
=
7. Arithmetic operations
3. Scales
11. Path
8. Connections
4. Distance
ALL 13 PUZZLES TOGETHER:
PART 1-2-3-4-5 DIVIDING
Divide the grid into five areas of different sizes (from 1 to 4 or 5). Then use the area’s sizes
as digits to form number for each row. The continuous block from a few cells of one area in
one row gives only one digit. Sum of the numbers is given.
4
1
4
4
5
4
5
3
1453
4
5
3
453
5
3
53
2
2010
45
2
2010
Answer key: write the three top numbers. For the example the answer would be: 4, 45, 1453