International Contest-Game Math Worksheet With Answers - Grade 5 And 6, Kangaroo, 2007 Page 2
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85. The square in the figure is a mini-sudoku: the numbers 1, 2, and 3 must
be written in the cells so that each of them appears in each row and in
each column. Harry started to fill in the square. In how many ways can
he complete the task?
A) 1
B) 2
C) 3
D) 4
E) 5
Solution: The number 3 must complete the second row as well as the first column, because the
other two digits are already written there. It is not allowed to have the same digit written more
than once in a row/column. Hence, in the second column, the number 3 can only be in the first
row (where the “?” sign is). There is only one way to complete the task.
Answer: A.
6. Basil, who is older than Peter by one year minus one day, was born on January 1, 2002.
What is the date of Peter’s birthday?
A) January 2, 2003
B) January 2, 2001
C) December 31, 2000
D) December 31, 2002
E) December 31, 2003
Solution: Basil is older, so Peter was born after Basil (in time). We need to add to Basil’s
birthdate 1 year (so we get January 1, 2003) and then to take off a day. Peter was born on
December 31, 2002.
Answer: D
7. A robot starts walking on the table from square A2 in the direction of
the arrow, as shown on the picture. It always goes forward. If it reaches
a barrier, it always turns right. The robot will stop if it he cannot go
forward after turning right. On which square will it stop?
A) B2
B) A1
C) C3
D) D1
E) It will never stop
Solution: By the rule given, the robot will follow the route: A2-B2-B1-A1-A2-A3-A4-B4-BC4-
D4-D3-D2-D1 and here, it will stop since it can’t turn to the right.
Answer: D
8. The Carpenter’s shop has two machines A and B. A is a “printing machine” and B is a
“turning machine”. What is the right sequence to obtain Figure 1 starting from Figure 2?
Figure 1
Figure 2
A) BBA
B) ABB
C) BAB
D) BA
E) BABBB
Solution: Figure 2 must be marked and then, rotated on 90°. Machine A does the marking,
while Machine B rotates on 45°.
Answer: B.
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