2006 inaemic math puzzle game eng
INAEMIC 2006 Puzzle Competition
Introduction:
Your team has 90 minutes to solve the following five problems. Team
members may discuss with one another. For Problem 1 to 4, record your
solutions on the answer sheet. For problem 5, raise your hand whenever
you have found a solution. Each problem is worth 20 marks and partial
credits may be obtained.
Ⅰ Below are the 12 pentominoes and a game board. Place four different
pentominoes on the board so that none of the other eight can be placed.
Pentominoes may be rotated and/or reflected. You must follow the grid
lines.
（20 points（
Marking Scheme
If another piece may be added, the score is 0. Otherwise, the score is 20 for
4 pieces and 5 is deducted for each additional pieces above 4. Negative
scores are adjusted to 0.
Ⅱ
Divide the grid into the fewest
number of squares along the grid
lines.
Squares can not overlap. (20 points)
Marking Scheme
If any piece is non-square, the score is 0. Otherwise, the score is 20 for 13
pieces or under, and 2 is deducted for each additional pieces above 13.
Negative scores are adjusted to 0.
N
1
3
3
9
E
W
?
Ⅲ
1
2
S
A 5 by 5 square has 36 grid points, 20 on the boundary and 16 in the interior.
Four sensors, N, E, W and S, are located on four different grid points. Five
alien spaceships, #1, #2, #3, #4 and #5, are landing at five different spots.
Each landing spot is on one of the 32 grid points other than the locations of
the sensors. A spaceship is detectable by a sensor unless the line joining the
location of the sensor and the landing spot of the spaceship is blocked by the
landing spot of another spaceship. The diagram shows the locations of the
sensors and the landing spot of spaceship #3. This spaceship is detectable by
all sensors except possibly S, since the line of vision may be blocked by
another spaceship landing on the spot marked by “?”. The total of the
numbers on the spaceships detectable by N, E, W and S are 13, 10, 9 and 12,
respectively. Determine the landing spots of spaceships #1, #2, #4 and #5.
Marking Scheme
The score is 5 for each sensor which can detect spaceships whose numbers
add to the prescribed value.
1
0
Ⅳ
Locate five buildings with heights 1, 2, 3, 4, 5 into every row and every
column of the grid, once each. The numbers on the four sides tell you how
many buildings can be seen from that side, looking row by row or column
by column. You can see a building only when all the buildings in front of it
are shorter.
(20 points)
10
1
12
2
5
4
11
3
13
Marking Scheme
If the arrangement does not fit the rule (not a Latin square), the score is 0.
Otherwise, the score is 5 for each side in which the total numbers of
buildings observable from that side agree with the prescribed value.
Ⅴ
Use all 6 pieces to make a shape with symmetry which can fit inside a
2×2×4 box. A shape is symmetrical if it maintains its original position after a
rotation or a reflection.
(20 points)
A
B
D
C
E
F
Marking Scheme
The score is 1 point for each distinct solution. Two solutions which are
obtainable from each other by a reflection or a rotation are not different.
INAEMIC 2006 Puzzle Competition
Answer Sheet
Team _______________________________________
1.
2.
Score ________________
3.
N
1
3
3
9
E
W
1
0
1
2
4.
S
10
1
12
2
5
4
11
3
13
5. Please raise up your hand after you have completed one shape.
The inspector will check and mark down the points.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
1. Cut off the color pentominoes and paste in the corresponding square of the board on
answer sheet.
.
2. Divide the below grid into squares along the grid lines and paste in the corresponding
square of the board on answer sheet. You must have a plane before you cut off the grid.
You can not combine the separate squares which are already cut from the grid.
Solution
1.
2.
3.
4.
10
13
1
4
3
5
2
3
1
2
4
5
12 2
5
3
5
1
4
2
4
3
1
4
5
1 2
13
3
3
9
10
1
5
4
12
4 pentominoes
5.
13 squares
(1)
(2)
C
C
A
E
D
D
D
F A
B
A
B
E
C
F
F
(5)
B
(3)
F
E
E
A
C
C
C
(9)
C
D
D
F
D
B
E
F
F
D
E
D
E
F D
E
A
E
A
C C B B
F
F
E
(13)
E
E A
B
A
E
E
A
E E
F
B
F
A D
B B C C
F
F
A
A
B
A
(10)
A
B
E
(14)
D
C
C
D
C
E
B B F
E
E
A
A
D
D
D
D
A
E
A
E
F
F
B
A
B
C
C
D
A
C B
F
B B C C
E
F
F
C
B
F
C
F
D
F
F
B B
F
E
B
E
F
F
(12)
F
F
E
B
A
F
F
D
C
B
A
D
A
E
A
C
C
D
D
E
E
B
E
E
C
A
D
D
A
E
F C C
A
C
D DA A
F D B B
B
C
C
C
C
E
F
C
C
D
D DA A
E
F
F
F
D
F
B
C
E
F
B
E
B
E
B
B
D DA A
C
D
E
A
F
B
B
F
F
C
C
E
A
D
B
D
C
C
(16)
E
B
F
B
B
A A
F
D D A A
C
C
E
B
C
E
F
CD D
(15)
A
D
D
F A A C
B
B B D
(11)
D
E E
A
E
(8)
E
B
C C
D D
(7)
E
A
(4)
A AD D
E
C
(6)
A A
B
B
2
F
F
B
1
1
(17)
F
A
F
F
B
A C D D
E
E
A
C
B
C
B
D
E
(18)
F
F
B
C
(19)
F
C
B
C
A
D E
E
E
C
B
B A A
D
D
C
A
C
E
B B F
A
A
E
D
F
F
E
D
D
(20)
B
E
A
E
B
E
A
D
A
B C C
F F
D
D
C
F
Introduction:
Your team has 90 minutes to solve the following five problems. Team
members may discuss with one another. For Problem 1 to 4, record your
solutions on the answer sheet. For problem 5, raise your hand whenever
you have found a solution. Each problem is worth 20 marks and partial
credits may be obtained.
Ⅰ Below are the 12 pentominoes and a game board. Place four different
pentominoes on the board so that none of the other eight can be placed.
Pentominoes may be rotated and/or reflected. You must follow the grid
lines.
（20 points（
Marking Scheme
If another piece may be added, the score is 0. Otherwise, the score is 20 for
4 pieces and 5 is deducted for each additional pieces above 4. Negative
scores are adjusted to 0.
Ⅱ
Divide the grid into the fewest
number of squares along the grid
lines.
Squares can not overlap. (20 points)
Marking Scheme
If any piece is non-square, the score is 0. Otherwise, the score is 20 for 13
pieces or under, and 2 is deducted for each additional pieces above 13.
Negative scores are adjusted to 0.
N
1
3
3
9
E
W
?
Ⅲ
1
2
S
A 5 by 5 square has 36 grid points, 20 on the boundary and 16 in the interior.
Four sensors, N, E, W and S, are located on four different grid points. Five
alien spaceships, #1, #2, #3, #4 and #5, are landing at five different spots.
Each landing spot is on one of the 32 grid points other than the locations of
the sensors. A spaceship is detectable by a sensor unless the line joining the
location of the sensor and the landing spot of the spaceship is blocked by the
landing spot of another spaceship. The diagram shows the locations of the
sensors and the landing spot of spaceship #3. This spaceship is detectable by
all sensors except possibly S, since the line of vision may be blocked by
another spaceship landing on the spot marked by “?”. The total of the
numbers on the spaceships detectable by N, E, W and S are 13, 10, 9 and 12,
respectively. Determine the landing spots of spaceships #1, #2, #4 and #5.
Marking Scheme
The score is 5 for each sensor which can detect spaceships whose numbers
add to the prescribed value.
1
0
Ⅳ
Locate five buildings with heights 1, 2, 3, 4, 5 into every row and every
column of the grid, once each. The numbers on the four sides tell you how
many buildings can be seen from that side, looking row by row or column
by column. You can see a building only when all the buildings in front of it
are shorter.
(20 points)
10
1
12
2
5
4
11
3
13
Marking Scheme
If the arrangement does not fit the rule (not a Latin square), the score is 0.
Otherwise, the score is 5 for each side in which the total numbers of
buildings observable from that side agree with the prescribed value.
Ⅴ
Use all 6 pieces to make a shape with symmetry which can fit inside a
2×2×4 box. A shape is symmetrical if it maintains its original position after a
rotation or a reflection.
(20 points)
A
B
D
C
E
F
Marking Scheme
The score is 1 point for each distinct solution. Two solutions which are
obtainable from each other by a reflection or a rotation are not different.
INAEMIC 2006 Puzzle Competition
Answer Sheet
Team _______________________________________
1.
2.
Score ________________
3.
N
1
3
3
9
E
W
1
0
1
2
4.
S
10
1
12
2
5
4
11
3
13
5. Please raise up your hand after you have completed one shape.
The inspector will check and mark down the points.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
1. Cut off the color pentominoes and paste in the corresponding square of the board on
answer sheet.
.
2. Divide the below grid into squares along the grid lines and paste in the corresponding
square of the board on answer sheet. You must have a plane before you cut off the grid.
You can not combine the separate squares which are already cut from the grid.
Solution
1.
2.
3.
4.
10
13
1
4
3
5
2
3
1
2
4
5
12 2
5
3
5
1
4
2
4
3
1
4
5
1 2
13
3
3
9
10
1
5
4
12
4 pentominoes
5.
13 squares
(1)
(2)
C
C
A
E
D
D
D
F A
B
A
B
E
C
F
F
(5)
B
(3)
F
E
E
A
C
C
C
(9)
C
D
D
F
D
B
E
F
F
D
E
D
E
F D
E
A
E
A
C C B B
F
F
E
(13)
E
E A
B
A
E
E
A
E E
F
B
F
A D
B B C C
F
F
A
A
B
A
(10)
A
B
E
(14)
D
C
C
D
C
E
B B F
E
E
A
A
D
D
D
D
A
E
A
E
F
F
B
A
B
C
C
D
A
C B
F
B B C C
E
F
F
C
B
F
C
F
D
F
F
B B
F
E
B
E
F
F
(12)
F
F
E
B
A
F
F
D
C
B
A
D
A
E
A
C
C
D
D
E
E
B
E
E
C
A
D
D
A
E
F C C
A
C
D DA A
F D B B
B
C
C
C
C
E
F
C
C
D
D DA A
E
F
F
F
D
F
B
C
E
F
B
E
B
E
B
B
D DA A
C
D
E
A
F
B
B
F
F
C
C
E
A
D
B
D
C
C
(16)
E
B
F
B
B
A A
F
D D A A
C
C
E
B
C
E
F
CD D
(15)
A
D
D
F A A C
B
B B D
(11)
D
E E
A
E
(8)
E
B
C C
D D
(7)
E
A
(4)
A AD D
E
C
(6)
A A
B
B
2
F
F
B
1
1
(17)
F
A
F
F
B
A C D D
E
E
A
C
B
C
B
D
E
(18)
F
F
B
C
(19)
F
C
B
C
A
D E
E
E
C
B
B A A
D
D
C
A
C
E
B B F
A
A
E
D
F
F
E
D
D
(20)
B
E
A
E
B
E
A
D
A
B C C
F F
D
D
C
F