Università degli Studi
di Milano
Dipartimento di
Matematica
"F. Enriques"
Kangaroo contest in Genoa 2004
1. I have a max/min thermometer in my greenhouse. It records both the highest and the lowest
temperatures reached from the time I reset it. I reset it on Sunday when the temperature was
4°C. Overnight the temperature fell 5°. Then during Monday it rose by 6° before falling 10°
during the night. On Tuesday it rose by 4° and fell 2° overnight. On Wednesday it rose 8°
during the day. When I looked at it on Wednesday evening, what were the maximum and
minimum temperatures recorded?
A) 12° and − 6°
B) 1° and − 9°
C) 10° and 0°
D) 5° and 4°
E) 5° and − 5°
16
is unusual since the digit 6, which occurs on both the top and the bottom, can
64
1
16
be “cancelled” to give
and this is equal to
. Which of these fractions has a similar
4
64
property ?
12
13
15
19
24
A)
B)
C)
D)
E)
24
39
45
95
48
2. The fraction
3. Humphrey the horse at full stretch is hard to
match. But that is just what you have to do: move
one match to make another horse just like (i.e.
congruent to) Humphrey. Which match must you
move?
A) A
B) B
C) C
D) D
E) E
A
D
C
B
E
4. Ahmed, Brian, Chloe, Danielle, Ethel, Francis and George have to choose a Form Captain from
among themselves. They decide to stand in a circle, in alphabetical order, and to count round (in
the same order) rejecting every third person they come to; that person then leaves the circle. The
last one left is to be Form Captain. Ahmed is eventually elected Form Captain. Where must the
counting have started (i.e., which person has been the first one to be counted)?
A) Ahmed
B) Brian
C) Danielle
D) Ethel
E) George
1
5. I am standing behind five pupils
who are signalling a five-digit
number to someone on the
opposite side of the playground.
From where I am standing the
number looks like 23456. What
number is actually being
signalled?
A) 42635
B) 45632
C) 53624
D) 62435
E) 65432
2
4
3
5
6
6. In 1742 Christian Goldbach (German, 1690 – 1764) wrote a letter to Leonard Euler (Swiss,
1707 – 83), saying that he believed every even number greater than 2 can be written as the sum
of two prime numbers. How many different ways are there of writing the number 42 as the sum
of two prime numbers? (Note: 3 + 5 and 5 + 3 would not be considered to be different ways of
writing the number 8.)
A) 1
B) 2
C) 3
D) 4
E) more than four
7. If the shading of squares is continued so that m and m’ become
lines of symmetry of the completed diagram, what is the largest
possible number of squares left unshaded?
A) 5
B) 7
C) 9
D) 11
E) 17
8. If U + V =1 and U2 + V2 = 2
A) 4
B) 8
C) 1
9. What is
then U4 + V4 = ?
D) 3
m
m’
E) 3,5
1
1
1
1
+
+
+
equal to ?
1× 2 2 × 3 3× 4 4 × 5
10. Evaluate 123123 ÷ 1001
140°
11. What is the size of the angle x in the diagram on right?
x
140°
140°
2
12. In the game Fizz-Buzz, players take turns to say consecutive whole numbers starting at 1; but in
place of each number which contains the digit “5” or which is divisible by 5 one has to say
“Fizz”, and in place of each number which contains the digit “7” or which is divisible by 7 one
has to say “Buzz”. How many numbers from 1 to 50 (both included) do not get replaced by
“Fizz” or “Buzz”?
13. Which of the shaded rectangles has
the larger area ?
14. Three “quarter circles” and one “three-quarter circle” – all of radius
10 cm – make this attractive “jug” shape. What is its area?
15. The solid cube has had its corners cut off to create three new
“corners” at each old “corner”. If the 24 corners are jointed to
each other by diagonals, how many of these diagonals lie
completely inside the “new solid” (except for the end-points) ?
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