Circular Maze

ZEKÂ OYUNLARI ÞAMPÝYONASI BELÝRÝO
PRIOR PUZZLE CHAMPIONSHIP
1. City Maze
1
2. Hunted
2
3. Matches
3
4. Irrigators
4
5. Earthworms
5
6. Connected Pairs
6
7. Torto Backwards
7
8. Twins
8
9. Fences Outside
Bu sorular, 16. Dünya
Zekâ
Oyunlarý
Þampiyonasý resmî
internet sitesinde 27
Eylül 2007 akþamý
yayýnlanan k itapçýk
temel alýnarak hazýrlanmýþ ve 3 Ekim 2007
sabahý tamamlanmýþtýr.
Soru isimleri ve
yönergeler, yayýnlanan
kitapçýktan alýntýdýr.
Cihan Altay
Serkan Yürekli
Gülce Özkütük
Mehmet Murat Sevim
10
10. Hexagonal Password Path
11
11. Circular Arrows
12
12. Circular Sudoku
13
13. Circular Easy as ABC
16
14. Circular Skyscrapers
18
15. Circular Fences
19
16. Circular Maze
21
17. Circular Tree-Tents
23
18. Circular Minefield
25
19. Four Winds in Faces
27
These puzzles are based
on the booklet published
on the official website of
the 16th World Puzzle
Championship on the
evening of September
27th 2007. They are
finished on October 3rd
2007 morning. Puzzle
names and instructions
are from those in the
booklet.
Cihan Altay
Serkan Yürekli
Gülce Özkütük
Mehmet Murat Sevim
Eklemeler/Addenda
Ýlk 10’un yarýþacaðý Yarý
Final’deki soru tipleri.
--9 Ekim 2007
20. Tri-Fences
28
21. Railroad Track
30
22. Doors
31
23. Balloon Balance
32
24. 3D Maze
33
25. Rotator Mosaic
34
26. Biggest and Smaller
35
Çözümler/Solutions
36
Puzzle types in the Semi
Final for the top 10.
--October 9th, 2007
City Maze
When you travel to these cities, you have to visit every house. Every time you arrive at a house, you must turn 90
degrees and you cannot pass through a tree. Draw a continuous loop (its sections connect the centres of the
neighbouring squares by a straight line) showing the path you made. The loop must not touch or cross itself.
1
Hunted
The goal is to distribute the Indians on the grid (in the empty squares) so that they can hunt all the animals. Each
Indian can capture, with his bow and arrows, all animals within 3 squares away from him, in any direction (line,
column and diagonals).
Each animal can only be captured by one Indian, and no Indian can be within the reach of another Indian’s arrow.
The number of Indians appears to the side of the diagram.
2
Matches
The goal is to find out which segments of matches placed on the tablecloth (grid made of hexagons) are burnt
(painted) and which aren’t (white). The flame always burns the match from the head (round side) to the base (square
side) - the flame never skips a segment. The flame from the segment of match burns the part of the tablecloth
(hexagon) where it is. The matches have different sizes and may be completely burnt, partially burnt or completely
new. The numbers around the tablecloth indicate the quantity of burnt segments in each column or diagonals. The
tablecloth will always have only one burnt piece and one unburnt piece (the burnt or unburnt areas have to be full
pieces). The numbers around the tablecloth indicate how many match segments are burnt in each line pointed out
by the arrows. A [=] sign indicates that the pointed lines have the same number of burnt segments, and a [=/] sign
indicates that the lines have a different amount of burnt segments.
4
1
2
1
3
1
4
3
5
3
Irrigators
The goal is to distribute the irrigators on the squared field. The numbers below the columns represent how
many irrigated squares there are in those columns, and the numbers on the right indicate how many irrigators
there are on those lines. One square cannot be irrigated by more than one irrigator, nor contain two irrigators.
There are two types of irrigators: the x-shaped ones and the +-shaped ones, and both irrigate just the first square
to where each of their “arms” points.
1
1
3
3
2
1
1
1
4 0 4
2 0 4 1 5 3 3 0 2
0
2
2 6 4
3
4
1
1
1
3
5 2 6 5 3 6 4 5 2 2
4
Earthworms
The grid represents a garden full of worms. The numbers on the left and above represent how many different
worms are found, respectively, in each line and column. The numbers on the right and below indicate how many
turns the worms make in each line and column. Each empty square must be filled in with a segment of one
worm. The points in the grid indicate the extremities (beginning and end) of all worms. The goal is finding out
how the worms are distributed.
3 2
1 2 3 2 2 2
3
2
3
4
2 4 4 4 2 1
3 3 4 4 3 3 3
3
3
3
4
3
3
2
2
4
1
3
5
2
2
3
4
4
3
2
1 2 3 3 2 2 2
2
2
3
4
3
3
2
5
2
4
4
4
5
3
3 5 4 5 3 4 3
6
4
5
2
3
2
4
2 3 4 4 5 4 4
5
Connected Pairs
Some symbols are placed in the grid. The goal is to connect them in pairs, using lines (horizontal and vertical, but
never diagonal, and always passing through the squares). All free squares can be used one single time, and the
same symbols cannot be connected. The pairs connected are fixed in the puzzle, that is, a symbol [*] connected to
a symbol [#] form a pair [*#], and every time those symbols appear again, they have to form the pair [*#]. The lines
cannot touch themselves nor lines that connect the same pair.
J
Ý
R
r
v
r
z
Ý
r
JR
z
z
z
v
Ý
vÝ
Ý
z
R
Jr
R
R
vJ
JR
Ýv
J
v
r
z
Ý
v
J
J
S
R
u
u
R
Ý
z
r
v
6
S
r
z
r
Torto Backwards
Torto is a very popular cultural puzzle in Brazilian magazines. This version, unfortunately, is not cultural: you must
connect characters to form a word in Tupi, language used by ancient Brazilian Indians. The rules are as follows:
connect vertical, horizontal and diagonal adjacent characters. You cannot jump a character, or cross a path already
made, and you cannot use the same character twice. To make it easier, a lot of words in Tupi are already found, but
some of them cannot be found in the diagram. Tell us which words cannot be found in the diagram, according to
the rules.
U
Y
M
A
S
T
P
I
B
O
K
I
T
E
I
A
N
U
N
A
R
A
G
E
U
I
P
U
M
K
7
IAGUAR
KAAPIUARA
MBOI
PIRA
SOO
TAPYR
ASU
BERABA
KATU
MIRI
PANEMA
ETA
IUB
OBY
PIRANG
TING
UNA
ABA
KARAIB
KUNATAI
Twins
Skyscrapers:
The grid symbolizes a neighborhood. Each row and column contains buildings of different heights. The numbers
outside the grid indicate how many buildings are visible from that direction (the higher buildings hide the lower
ones behind them). The numbers in brackets indicate the minimum and maximum building height for that grid.
Simple as ABC:
Fill in the letters in the diagram. Each letter occurs once in each of the rows and columns. The letters outside the
diagram indicate the letters you come across first from that direction. The letters in brackets indicate the minor and
greater letters for that grid (in alphabetical order).
Twins:
In each pair (Skyscrapers and Simple as ABC) each letter corresponds to a number. The letters occupy the same
position, in the grid, as their corresponding numbers.
1-5
A-E
3
2
2
C
1
2
2
1
2
1
3
E
D
B
E
1 3
3
D
B
D
4
2
B
CE
D
2
1
E
E
D
C
4
B
2 2 4
8
C
E
A
3
3
3
4
1
2
2
2
E
C
C
3
A
2 3 2
AD
1-7
A-G
1 3
1
2
4
3
4
4
3 3
1
3
G
A
E
4
2
3
3 4 1
FEDC
6
3
5
5
E
2
A
C
3
9
A
F
F
B
AEE
C
E
F
A
F
B
Fences Outside
This puzzle is similar to traditional fences (draw a single-closed path or loop without crossing or overlapping), but
the hints are given outside the grid. Each number shows how many segments of the path there are in the given
direction.
1
3
1
1
2
3
3
1
1
2
3
2
1
1
2
4
5
10
5
1
1
2
3
5
5
Hexagonal Password Path
Starting in the first password gray letter and finishing in the last, draw a path connecting the letters of the password
in the sequence of reading. When you finish the first word, start again and so on. The path can travel through the
edges and it passes through all hexagons, without crossing or overlapping.
R R I O
O I O I R
R R I O R I
I R O
I R O
O I R O O R
O I O R I
R I I O
R R R I
I O I O O
R O O R I R
R O I
O I I
R O R I I O
I I R O R
O R I O
RIO
RIO
11
Circular Arrows
In each empty cell on the inner border and on the outer border, insert an arrow pointing at one of the three possible
neighbor cells that contain numbers. Each number in the grid indicates the number of arrows pointing at it.
3
1
0
2
0
2
3
3
1
3
3
1
1 3
1 1
2 2
4
4
3
3
1
2
2 1
1
2
4 0
2 3
1
0
3
2
1
2
2
1
5 2
1
3 4
2
1
2
3
3
3
12
3
3
1
Circular Sudoku
Fill the grid with numbers 1 to 9 (1 to 4 in the example) so that every number appears in each annulus, sector and
outlined region.
7
1
8
8
5 6
9
5
9
1
9 1
4
3
2
6 9
6
4
8
2
3
8
9
7
7
2
2
7
6
4
5
2
9
6
13
2
2
1
3
3
9
8
1
1
9
6
7
6
3
8
7
9
4 8
7
6
2
4
5 9 2
5
9
8
7
3
6
14
1
8
9
8
9
3
5
8
7 5
9
2
1
7 4
5
5
2
2 6
6
3
8
7
6
1
7
9
15
8
3
Circular Easy as ABC
Fill the grid with letters A, B, C (or A, B, C, D), so that each circular sector and annulus contains exactly one instance
of all these symbols. Letters outside the grid and at the top circular sector appear first in corresponding directions.
C
C
A
A
B
16
B
C
C
A
B
A
B
A
B
C
C
17
Circular Skyscrapers
Fill the grid with numbers 1, 2, 3, 4 (or 1, 2, 3, 4, 5), so that each circular sector and annulus contains exactly one
instance of all these numbers, representing the height of buildings in a neighborhood. Numbers at the inner and
outer annulus and at the top circular sector show the number of visible skyscrapers from that direction (the higher
buildings hide the lower ones behind them). At the annulus, use the same logic, considering a curved view along
the annulus.
3
3
2
3
4
2
4
2
4
4
18
4
Circular Fences
Draw a single continuous loop along the lines of the grid. The loop may not touch or cross itself. Each number shows
the number of sides of the cell used by the loop.
1
1
1
1 1
0
1
1
1
0
1
1
0
1
1
19
3
1
1
2
2
3
2
2
2
3
1
2
3
2
2
3
2
2
2
3
2
3
1
1
2
3
2
2
3
1
2
2
1
2
3
1
3
1
1
2
2
1
1 2
2
3
3 1
2
2
1
1
20
1
3
2
2
2
1
3
2
2
2 1 2
1 2
3
3
2
1
2
1
2
1 1
2
2
1
1
1
2
1 1 3
1 2
2
2
2
3
2
2
2
1
1
2
Circular Maze
Draw a single continuous loop that passes through every cell of the grid that doesn’t contain a black circle. The
loop may not touch or cross itself.
21
22
Circular Tree-Tents
Locate all the tents in the grid. Each tree is exactly connected to only one tent. A tent can be found in the same
annulus or sector, adjacent to the tree. Tents are never placed adjacent to each other vertically, horizontally,or even
diagonally. The numbers outside the grid and at the top sector give the total number of tents in the corresponding
annulus or sector.
3
1
3
1
3
1
1
2
2
3
1
1
3
2
2
3
2
2
1
3
23
3
2
1
2
2
1
2
2
2
3
2
3
3
1
3
1
1
3
1
2
24
Circular Minefield
Place bombs in the grid. The numbers in each cell indicate the number of mines around that particular number.
No bomb can be placed in the cells that contain numbers.
4
3
4
5
3
3
2
3
1
2
4
2
1
0
4
4
0
4
3
3
2
25
1
2
1
1
5
3
0
4
3
4
3
2
3
2
2
5
2
2
1
5
1
3
1
1
4
1
2
2
1
3
3
2
2
5
2
2
3
1
6
3
2
4
4
3
1
3
2
2
26
4
2
1
3
Four Winds in Faces
A Four Winds diagram was divided and glued to the faces of different pieces, being possible that the pieces also
received false parts. The aim is to correctly solve the Four Winds, but, in order to do that, it’s necessary to find the
correct position for each piece. All faces of all pieces contain one letter that identifies them. Ignore those letters to
solve the Four Winds. The rules to Four Winds are the traditional ones:
- Draw horizontal or vertical lines, starting from squares that contain numbers;
- The numbers always represent the addition of the length of the lines that start in that square;
- Lines can’t overlap, and always pass through the center of the empty square;
- All squares have to be used.
To find out the correct assembling of the pieces, the following rules should be observed:
- All pieces must be used;
- Pieces must be positioned orthogonally in relation to the others;
- All visible faces should be used.
1
6
4
9
17
2
4
10
2
2
2
6
2
8
2
2
Üç Küp/Three Cubes
4
4
5
2
1
5
27
Tri-fences
Three single closed loops (exactly like Fences puzzles) can be drawn over the dotted lines in the diagram and have
exactly the same shape (can be rotated but not mirrored). Each number shows how many segments are used in
that square. The three fences cannot touch each other, not even diagonally.
1
1
1
0
2
1
0
1 2
0
1
1
2
1
1
1
1
1 0
2
2
3
3
1
2
2
4
28
3
0
3
3 3
2
0
0
3
2
1
1 2
29
Railroad Track
Lay a single, closed loop of railroad track that levels through every cell of the grid. The track connects cells horizontally
or diagonally, and crosses itself only in the cells with crosses (all the crossings are already placed). The track does
not turn as it passes though the stations (which are the cells containing numbers) nor crosses. As you follow the
track, visit all stations in numerical order and return to the first station.
1
3
5
6
4
2
3
1
8
7
5
6
2
7
4
3
4
6
5
2
9
1
8
30
Doors
The floor has been divided into many rooms, which are all interconnected by doors. Some doors are open, others
are closed. The rooms have numbers indicating how many other rooms can be looked into. Which doors are closed?
5 4 4 6
5 4 5 5 3
3 5 6 7 4 4
4 4 6 6 4 4 4
5 3 7 7 6 5
9 7 5 6 5
6 6 4 7
2 3 5 1
5 6 6 8 7
7 5 4 2 6 4
1 4 1 3 4 2 3
5 9 5 8 7 7
2 6 4 3 4
4 7 3 1
9 2 6 2 8
3 7 11 4 6 5
5 1 8 6 4 1 6
4 6 3 10 14 5 7 8
6 5 4 4 9 6 3 5 7
6 2 3 2 7 7 2 3
5 1 2 6 5 6 1
4 2 3 1 3 8
8 5 4 5 7
31
Balloon Balance
Add the weights and balloons to the diagram (in the white circles) so that the entire mechanism is in equilibrium.
As happens with normal balance puzzles, the total torque at each fulcrum must be zero.
1 2 3 4 5
1 2 3 4 5
5
1 2 3 4 5 6
1 2 3 4 5 6
6
4
32
3D Maze
Cross the maze from A to B, through the different levels. It’s only possible to change levels through the holes (white
quadrilaterals).
A
B
B
A
33
Rotator Mosaic
Divide the grid (along the grid lines) into exactly 10 symmetric pieces (each appearing unchanged if rotated 180
degrees, including its shape and the pattern of any white or black disks). There are no two equal shapes (independent
of the pattern).
9 parça/9 pieces
34
Biggest and Smaller
Place the numbers into the white cells so that the numbers in the gray cells are the sum of the numbers in the
neighbouring white cells. The black arrows show the biggest of the neighbouring numbers (linked by the gray cell)
and the white arrows show the smallest ones.
1-16
46
30
19
31
24
33
33
18
38
1-16
28
26
32
16
14
43
36
27
1-25
74
56
24
38
13
44
30
69
53
35
54
32
ÇÖZÜMLER
SOLUTIONS
36
3
4
1
1
4
2
3
1
5
1
1
3
3
2
1
1
1
4 0 4
2 0 4 1 5 3 3 0 2
0
2
2 6 4
37
3
4
1
1
1
3
5 2 6 5 3 6 4 5 2 2
3 2
1 2 3 2 2 2
3
2
3
4
2 4 4 4 2 1
3 3 4 4 3 3 3
3
3
3
4
3
3
2
2
4
1
3
5
2
2
3
4
4
3
2
1 2 3 3 2 2 2
2
2
3
4
3
3
2
5
2
4
4
4
5
3
3 5 4 5 3 4 3
6
4
5
2
3
2
4
2 3 4 4 5 4 4
38
J
Ý
R
r
z
r
z
Ý
r
JR
z
Ý
z
v
R
Ýv
J
Ý
R z
Ý
v
J
J
r
S
R
u
v
r
u
IAGUAR
KAAPIUARA
MBOI
PIRA
SOO
TAPYR
ASU
BERABA
KATU
MIRI
2 4
3
2
1 5
2 1
2
2
v
z
R
vJ
JR
vÝ
Jr
z
3
2 1
3 2 1 5
2 1 5 4 2
1 5 3 4 2
3 4 2 1 4
5 2 4 3
4 1 5 3
3 1 3
39
R
Ý
z
r
v
S
r
PANEMA
ETA
IUB
OBY
PIRANG
TING
UNA
ABA
KARAIB
KUNATAI
C B D
C BEDA
BBEDA C
D DABCEE
A BC EDD
DAECB B
EEC DAB
CE
1
5
1
3
2
4
4
1
2
2
1
2
4
3
4
1
2
4
3
5
3
2 3
3
1
5 4
1 5
4 2
2 2
3
2 1 5
1 2
5 4 3
4 3
3 5 1
2 4
2
1 3
4 7 3 2
7 4 6
5 4 7
6 1 4
3 5 2 1
2 3 7 5
6 1 5
1 2 6 3
5 3
4 2
4 5 1
5 2
3 1 4
2
1 3
4
D
E
BDCA EE
DDCA E B
AE DBCC
C BEAD
EADBC C
B BECDA
E
A
3 3
3 4 2
4 5 3
1 2
5 2 1 3
2 4
1 3 5
3 2
E E
CCDBEA
D CABE
B A E DCC
AE BCD
EBDC AA
CADEB
AD
3
1
5
2
7
6
4
3
3
6
2
1
3
7
3
5
16
3
24
FEDC
BFEDC AG
F B AGE DCC
GG B F D A C E E
A ACBFGED
EEGDCA B F F
DE FGBC AA
AACG EDB FF
CCDA E FGBB
AEE
3
6
5
4
1 6
2 4 7
7 5 43
4 1 2
40
1
3
1
1
2
3
3
1
1
2
3
2
1
1
2
4
5
R R I O
O I O I R
R I O R O I
O I O
I O R
I R R I R R
O O I R I
R I O O
3
1
0
2
3
3
0
2
1
1
2
3
5
5
1
0
3
3
1
R R R I
I O I O O
R O O R I R
R O I
O I I
R O R I I O
I I R O R
O R I O
3
1
1 3
1 1
2 2
4
4
3
3
1
2
1
2
1
2
0
4
2 3
5
2
1
2
2
1
5 2
1
3 4
2
1
41
2
3
3
3
3
3
1
3
2
9
8
7
6
5 6
1
4 9
5
1 3
4
7 8
2
9 1
6
7
2 5
4
3
3
2
8 7
9
8
1
5
4
6
7
1
8
2
9
5
5
6
4
7
9
4
1
6
3
3
2
8
6 1 4 8 9 5 7 3 2
9
7
4
5
4
2
8
6
3
7
1
3
8
4
6
2
9
1
2
3
4
6
8
9
9 8
1
6 7
7
5 1
5
4 2
3
2
6
1
8
3
9
4 3
5
8 7
7
5 6
4
1 2
9
4 1
7
6
2 8
9
9
3
3
6 5
5
7
1
2
4
8
5
7
9
4
1
2
6
6
4
3
3
8
8
1
7
1 2
5
7
4 6
8
4
7
3
3 9
5
2
9
8
1
6
9
2
5
3 5 4 1 9 2 6 8 7
2
6
5
9
8
7
2
8
5
4
4
6
1
3
3
7
9
1
42
5
7
1
4
7
3
4
5
2
2
9
9
8
6
6
8
3
1
4 8 7 3 6 5 9 2 1
9
5
6
2
9
4
8
7
1
7
3
3
6
8
3
2
5
4
C
A
C
-
A
C
B
A
A
C
B
-
B
A
C
B
C
-
-
D
A
B
-
A
B
A
C
A
-
C
C
C
B
-
C
C
A
A
C
B
B
C
B
B
C
A
D
B
A
B
A
-
B
A
B
-
C
D
A
D
A
B
C
C
-
B
4
5
1
A
-
4
2
4
2
2
-
C
D
3
5
4
2
3
1
B
4
3
3
2
1
3
1
4
3
4
2
2
3
1
3
2
4
1
2
4
5
3
43
1
4
3
2
4
4
4
1
2
3
5
4
5
1
2
3
1
1
1
1 1
0
1
1
1
1
0
1
0
1
1
3
1
1
2
2
3
2
2
1
1
2
2
1
1 2
1
1
2
2
3
3 1
2
2
1
1
1
3
2
2
2
1
3
2
2
3
3
1 1 3
1 2
2
2
2
3
2
2
2
1
1
2
44
1
2
3
2
2
3
2
2
3
1
2
2
1
2
1
3
2 1 2
1 2
2
1
3
2
1
2
1 1
2
2
1
3
2
2
2
2
3
1
1
2
3
2
3
45
3
1
3
1
3
1
1
2
2
3
1
1
3
2
2
3
2
2
1
3
3
2
1
2
2
1
2
2
2
3
2
3
3
1
3
1
1
3
1
46
2
4
3
4
5
3
3
2
3
1
2
2
1
4
3
0
0
4
4
4
3
4
3
4
0
3
1
1
5
1
2
2
3
2
3
2
2
5
2
2
1
5
1
1
1
4
3
3
1
2
2
2
5
2
2
1
2
3
3
1
6
3
2
4
4
3
3
47
1
2
2
4
2
1
3
1
6
4
9
17
2
4
10
2
2
6
2
2
2
2
8
4
4
5
2
1
5
48
1
1
1
2
0
2
1
0
1 2
0
1
1
2
2
1
1
3
1
1
3
1
2
1 0
4
3
0
1
3
3
3 3
5
2
0
2
6
0
3
2
1
4
2
1 2
7
3
1
8
3
4
6
7
5
5
2
9
6
2
1
8
4
49
5 4 4 6
5 4 5 5 3
3 5 6 7 4 4
4 4 6 6 4 4 4
5 3 7 7 6 5
9 7 5 6 5
6 6 4 7
2 3 5 1
5 6 6 8 7
7 5 4 2 6 4
1 4 1 3 4 2 3
5 9 5 8 7 7
2 6 4 3 4
4 7 3 1
9 2 6 2 8
3 7 11 4 6 5
5 1 8 6 4 1 6
4 6 3 10 14 5 7 8
6 5 4 4 9 6 3 5 7
6 2 3 2 7 7 2 3
5 1 2 6 5 6 1
4 2 3 1 3 8
8 5 4 5 7
2
4
1
3
5
2
3
5
1
50
4
5
6
4
6
5
3
1
4
2
3
2
1
B
A
A
B
51
15
10
11
14
46
31
33
13
8
2
6
30
24
18
4
5
9
1
19
33
38
7
13
10
3
9
8
16
14
12
12
20
21
19
23
11
12
13
14
25
74
22
56
38
44
69
10
2
1
17
16
52
24
13
30
53
9
3
54
32
43
24
18
7
6
5
4
15
32
8
1
16
28
16
36
7
3
4
15
26
14
27
11
5
2
6