IKMC grade 5 6 from 2005 to 2018

D It is impossible to determine To remove this notice, visit: www.foxitsoftware.com/shopping.5. To remove this notice, visit: www.foxitsoftware.com/shopping... To remove this notice, vi

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Phòng 302 nhà N3B – Bồi dưỡng toán tiểu học và THCS Thầy Quân 0868869670

Kangaroo 2005 — Benjamin Max Time: 60 min

2 Ali and Amna have 10 sweets, but Amna has 2 more than Ali How many

sweets does Amna have?

3 In the diagram any of the eight kangaroos can jump

to another square What is the least number of kangaroos that

must jump so that each row and each column has exactly two

kangaroos?

4 Ali lives with his father, mother, brother and also one dog, two cats, two

parrots and four goldfish How many legs do they have altogether?

5 A butterfly sat down on my correctly solved exercise

What number is the butterfly covering?

2005 − 205 = 25+

6 The diagram shows a cube with sides of length 12 cm

An ant is walking across the cube’s surface from A to B on the

route shown How far does it walk?

(D) It is impossible to determine

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7 Saima cut a sheet of paper into 10 pieces Then she took one of the pieces and

cut it into 10 pieces also She repeated this twice more How many pieces of paper did she

have in the end?

8 Aisha chose a whole number and multiplied it by 3 Which of the following

numbers could not be her answer?

4-Point-Problems

9 The five cards with the numbers from 1 to 5

lie in a horizontal row (see the figure) Per move, any two

cards may be interchanged Find the smallest number of the

moves required to arrange all cards in increasing order?

11 Raza needs 40 minutes to walk from home to the sea by foot and to return

home on an elephant When he rides both ways on an elephant, the journey takes 32 minutes

How long would the journey last, if he would walk both directions?

12 If the sum of five consecutive positive integers is 2005, then the largest of these numbers

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14 If you count the number of all possible triangles and the number

of all possible squares in the picture how many more triangles than

squares do you find?

15 Which of equalities means that m makes 30 % from k?

16 If you fold up the net on the right, which of these

cubes can you make?

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5-Point-Problems

17 Different figures represent the different digits Find the digit

corresponding to the square

18 In a trunk there are 5 chests, in each chest there are 3 boxes, and in each box there are

10 gold coins The trunk, the chests, and the boxes are locked How many locks must be

opened in order to get 50 coins?

19 A caterpillar starts from his home and move directly on a ground, turning after each hour at 90°

to the left or to the right In the first hour he moved 1 m, in the second hour 2 m, and so on At what

minimum distance from his home the caterpillar would be after six hours traveling?

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Benjamin: Class (5-6)

3-Point-Problems

1 3  2006 = 2005 + 2007 + Find the missing number

2 Six numbers are written on the cards, as

shown What is the largest number you can form with the given cards by placing them in

a row?

3 Four people can sit at a square table For the school party the students put together 10

square tables in order to make one long table How many people could sit at this long table?

4 Choose the picture where the angle between the hands of a watch is 150º

5 On the left side of Main Street one will find all odd house-numbers from 1 to 39 On the

right side the house-numbers are all the even numbers from 2 to 34 How many houses are there on the Main Street?

6 With how many ways one can get a number 2006 while following the

arrows on the figure?

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8 The cube in the figure has one of the following nets:

4-Point-Problems

9 We need 9 kg of ink to paint the whole cube How much ink

do you need to paint the surface of figure near the cube (see figure)?

10 What is the difference between the sum of the first 100 strictly positive even numbers and the

sum of the first 100 positive odd numbers?

11 A paper in the shape of a regular hexagon, as the one shown, is folded in such

a way that the three marked corners touch each other at the centre of the hexagon What is the obtained figure?

12 The diameter AB of the circle is 10 cm (as shown in figure) What

is the perimeter of the figure which is marked with dark line, if the rectangles in the figure are coincident?

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13 Which path is the shortest?

14 Ali is building squares with matches

adding small squares that it already has built according to the schema of the figure

How many matches does he have to add to

15 The first three letters of the word KANGAROO

are put in equal squares with length of side 2 (as shown in figure) Find a false statement

A perimeter of K is more than perimeter of A by 1

B perimeter of N is more than perimeter of A by 1

C perimeters of A and N are equal

D perimeters of K and N are equal

16 Find a truly end of the sentence: If I look on your reflection then

A your reflection looks on me

B my reflection looks on you

C my reflection looks on your reflection

D your reflection looks on mine reflection

5-Point-Problems

17 A rod of length 15 dm was divided into the greatest possible number of pieces of

different integer lengths in dm The number of cuts is:

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18 A river goes through a city and there are two islands There are

also six bridges as shown in the figure How many paths there are going out of a shore of the river (point A) and come back (to point B) after having spent one and only one time for each bridge?

1,2

1

3

2,2

1,31

20 What is the smallest number of dots that need to be removed from the

pattern shown, so that no three of the remaining dots are at the vertices

of an equilateral triangle?

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INTERNATIONAL KANGAROO MATHEMATICS CONTEST 2007

3-Point-Problems

Q1 Asia walks from the left to the right and puts the numbers in her basket Which of the following

numbers can be in her basket?

Q2 Which piece fits together with the given one to form a rectangle?

Q5 Usman, who is older than Ali by 1 year minus 1 day, was born on January 1, 2002 What is the

date of Ali’s birth?

D) December 31, 2002

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Q6 The Carpenter’s shop has two machines A and B A is a “printing machine” and B is a “turning

machine” What’s the right sequence to obtain starting from ?

Q7 If you cut a 1 meter cube into 1 decimeter cubes and put one on the other, what height this

structure will have?

Q8 Uzma cut a paper in the shape of a square with perimeter 20 cm into two rectangles The

perimeter of one rectangle was 16 cm What was the perimeter of the second rectangle?

4-Point-Problems

Q9 In a square grid Hina colours the small squares that lie on the two diagonals What is the size

of the grid if Hina altogether colours 9 small squares?

Q10 In three adjacent faces of a cube, diagonals are drawn as shown in the

figure Which of the following net is that of the given cube?

Q11 There were 60 birds at three trees In some moment 6 birds flew away from the first tree, 8

birds flew away from the second tree, and 4 birds flew away from the third tree Then there were the same number of birds at each of the three trees How many birds were there at the second tree at the beginning?

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Q12 Two 9 cm × 9 cm squares overlap to form a 9 cm ×13 cm rectangle as shown Find the area

of the region in which the two squares overlap.

Q13 Imran let a pigeon out at 7.30 a.m., to deliver a message to Saad The pigeon delivered the

envelope to Saad at 9.10 a.m A pigeon flies 4 km in 10 minutes What was the distance between Saad and Imran?

Q14 A parallelogram is divided in two parts P1 and P2, as shown in the

figure What sentence is surely true?

A12B (see the Fig.) Find the length of AA1A2 A12B.

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5-Point-Problems

Q17 Iqra is 10 years old Her mother Asma is 4 times as old How old will Asma be when Iqra is

twice as old as she is now?

Q18 To the right side of a given 2-digit number we write the same number obtaining 4-digit

number How many times the 4-digit number is greater than the 2-digit number?

Q19 Ahmed thought of an integer Umar multiplied it either by 5 or by 6 Ali added to the Umar’s

result either 5 or 6 Tahir subtracted from Ali’s result either 5 or 6 The obtained result was

73 What number did Ahmed think of?

once What is digit Y?

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Benjamin Level: Class (5 & 6) Max Time: 2 Hours

3)

Javed likes to multiply by 3, Parvaiz likes to add 2, and Naveed likes to subtract 1 In what

order should they perform their favorite actions to convert 3 into 14?

Numbers 2, 3, 4 and one more number are written in the cells of 2 × 2 table It is known

that the sum of the numbers in the first row is equal to 9, and the sum of the numbers in

the second row is equal to 6 The unknown number is

A) 5 B) 6 C) 7 D) 8

6)

Before the snowball fight, Ali had prepared a few snowballs During the fight, he made

another 17 snowballs and threw 21 snowballs at the other boys After the fight, he had 15

snowballs left How many snowballs had Ali prepared before the fight?

A) 53 B) 33 C) 23 D) 19

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×

35 63

30 ? What is the number in the square with the question mark ?

A) 54 B) 56 C) 65 D) 36

8)

In a shop selling toys a four-floor black and white “brickflower” is displayed (picture 1)

Each floor is made of bricks of the same colour On picture 2, the flower is shown from the

top How many white bricks were used to make the flower?

A) 9 B) 10 C) 12 D) 14

4-point problems

9)

With what number of identical matches it is impossible to form a triangle? (The matches

should not be broken!)

A) 7 B) 6 C) 5 D) 4

10)

There are 5 boxes and each box contains some cards labeled A, B, O, R, V as shown Peter

wants to remove cards from each box in such a way that at the end each box contains only one

card, and different boxes contain cards with different letters What card remains in box 5?

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A circular table is surrounded by 60 chairs n people are sitting at this table in such a way that

each of them is a neighbour of exactly one person The largest possible value for n is

A) 40 B) 30 C) 20 D) 10

13)

By shooting two arrows at the shown aiming board on the wall,

how many different scores can we obtain? (Missing the board is

possible.)

A) 4 B) 6 C) 8 D) 9

14)

Rabia has some CDs on a table She put them into three cases She put seven CDs into each,

but there were still two more CDs, which did not fit into those cases, so she left them on the

table How many CDs does Rabia have?

A) 23 B) 21 C) 20 D) 19

15)

Which of the “buildings” (A), , (E) – each consisting of

exactly 5 cubes – can you not obtain from the building on the

right hand side if you are allowed only to move exactly one

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16)

Points A, B, C and D are marked on the straight line in some order It is known that AB = 13,

BC = 11, CD = 14 and DA = 12 What is the distance between the farthest two points?

A) 14 B) 38 C) 50 D) 25

5-point problems

17)

One of the cube faces is cut along its diagonals (see the fig.) Which of the following

nets are impossible?

1 2 3 4 5

A) 1 and 3 B) 1 and 5 C) 3 and 4 D) 3 and 5

18)

Seven cards lie in a box Numbers from 1 to 7 are written on these cards (exactly one number

on the card) Two persons take the cards as follows: The first person takes, at random, 3 cards

from the box and the second person takes 2 cards (2 cards are left in the box) Then the first

person tells the second one: “I know that the sum of the numbers of your cards is even” The

sum of card’s numbers of the first person is equal to

A) 10 B) 12 C) 6 D) 9

19)

For each 2-digit number from 30 to 50, the digit of units was subtracted from the digit of tens

What is the sum of all the results?

A) 0 B) 15 C) – 5 D) – 15

20)

How many digits can be at most erased from the 1000-digit number 20082008…2008, such

that the sum of the remaining digits is 2008?

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International Kangaroo Mathematics Contest 2010

3-point problems

Q1) Knowing that ▲ + ▲ + 6 = ▲ + ▲ + ▲ + ▲, which number is hidden by ▲?

A) 2 B) 3 C) 4 D) 6

Q2) The number 4 is next to two mirrors so it reflects twice as shown When the same thing happens

to number 5, what do we get instead for the question mark?

A) B) C) D)

Q3) Kalim goes directly from Zoo to School He

counts each flower on the way Which of the

following number can not be his result School

Zoo

A) 9 B) 10 C) 11 D) 12

Q4) A ladder has 21 stairs Nadeem and Mahmood are counting stairs; one – from bottom to top,

another – from top to bottom They met on a stair that was called the 10th by Nadeem What number

will Mahmood give to this stair?

A) 13 B) 11 C) 12 D) 10

Q5) Adil has connected all the upper points to all the lower

points How many lines Adil has drawn?

A) 20 B) 25 C) 30 D) 35

Q6) A fly has 6 legs, while a spider has 8 legs Together, 2 flies and 3 spiders have as many legs as

10 birds and

A) 3 cats B) 4 cats C) 5 cats D) 6 cats

Q7) There are seven bars in the box It is possible to slide the bars in

the box so there will be space for one more bar At least how many

bars have to be moved?

A) 1 B) 2 C) 3 D) 4

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Q8) A square sheet of paper has grey upper side and white lower

side Sadia has divided it in nine little squares Along which does

she have to cut?

A) 1, 3, 5 and 7; B) 2, 4, 6 and 8; C) 2, 3, 5 and 6;

2 4

Q12) Bilal has selected a number, has divided it by 7, then added 7 and finally multiplied the sum

by 7 That way he comes up with the number 777 Which number was it he selected?

A) 111 B) 722 C) 567 D) 728

Q13) The numbers 1, 4, 7, 10 and 13 have to be written in the

picture so that the sum of three numbers in a row equal to the sum of

three numbers in a column What is the biggest possible sum?

A) 20 B) 21 C) 22 D) 24

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Q15) Esha has drawn a flower with 5 petals She wants to

colour the flower, but she has only 2 different colours –

red and yellow How many different flowers can Esha get

if she has to colour each petal using one of these 2

1

C) 5

1

D) 83

5-point problems

Q17) The picture shows a balanced mobile We neglect

weights of horizontal bars and vertical strings The total weight

is 112 grams What is the weight of the star?

A) 7 B) 12 C) 16 D) We can’t know

Q18) A pizza-shop offers a basic version of pizza with mozzarella and tomatoes One or two toppings

must be added: anchovies, artichokes, mushrooms, capers Moreover, for each pizza three different sizes

are available: small, medium, large How many different types of pizza are available at all?

A) 30 B) 12 C) 18 D) 48

Q19) A jeweller makes chains by connecting identical grommets (picture 1) Proportions of grommets

are shown on picture 2 What is the length of a chain which consists of 5 grommets?

A) 20 mm B) 19 mm C) 17.5 mm D) 16 mm

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Level Benjamin – Class 5 & 6

3 point problems

PROBLEM 01

Basil wants to paint the word KANGAROO He paints one letter each day He starts on Wednesday

On what day will he paint the last letter?

(A)Monday (B)Tuesday (C)Wednesday

A square of paper is cut into two pieces using a single straight cut

Which of the following cannot be the shape of either piece?

(A) a square (B) a rectangle (C) a right-angled

triangle

(D) a pentagon (E) an isosceles

triangle

PROBLEM 04

Hamster Fridolin sets out for the Land of Milk and Honey His way to the legendary Land passes

through a system of tunnels There are 16 pumpkin seeds spread through the tunnels, as shown in the

picture

What is the highest number of pumpkin seeds Fridolin can collect if he is not allowed to visit any

junction more than once?

(A)12 (B)13 (C)14 (D)15 (E)16

PROBLEM 05

In Crazytown, all the houses on the right side of Number Street have odd numbers However,

Crazytowners don't use numbers containing the digit 3, though they use every other number The first

house on the right side of the street is numbered 1, and the houses are numbered in increasing order

What is the number of the fifteenth house on the right side of the street?

(A)29 (B)41 (C)43 (D)45 (E)47

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PROBLEM 06

The picture shows a partially built cuboid

Which of the following pieces will complete the cuboid?

(A) (B) (C) (D) (E)

PROBLEM 07

We pour 1000 litres of water into the top of the pipework shown in the picture

Every time a pipe forks, the water splits into two equal parts How many litres of water will reach

container Y?

(A)500 (B) 660 (C)666.67 (D) 750 (E) 800

PROBLEM 08

The date 01-03-05 (1 March 2005) consists of three consecutive odd numbers in increasing order

This is the first date with this feature in the 21st century Including 01-03-05, how many dates in the

21st century, when expressed in the form dd-mm-yy, have this feature?

(A) 5 (B) 6 (C) 16 (D) 13 (E) 8

PROBLEM 09

The picture shows four cardboard pieces

All four pieces are put together without gaps or overlaps to form various shapes Which of the

following shapes cannot be made in this way?

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PROBLEM 10

When Liza the cat just lazes around, she drinks 60 ml of milk per day But each day that she catches

mice, she drinks a third more milk In the last two weeks she has been catching mice every other day

How much milk did she drink in the last two weeks?

(A)840 ml (B)980 ml (C)1050 ml (D)1120 ml (E)1960 ml

4 point problems

PROBLEM 11

Andrew wrote the letters of the word KANGAROO in cells He can write the first letter in any cell he

wants He writes every subsequent letter in a cell that has at least one point in common with the cell in

which the previous letter was written Which of the tables can Andrew not create in this way?

(A) (B) (C) (D) (E)

PROBLEM 12

All 4-digit integers with the same digits as the number 2011 are listed in increasing order (so each

number in the list has two 1s, one 0 and one 2) What is the difference between the two numbers

appearing on either side of 2011 in this list?

(A)890 (B)891 (C)900 (D)909 (E)990

PROBLEM 13

Four of the numbers on the left are moved into the cells on the right so that the addition is correct

Which number remains on the left?

(A)17 (B)30 (C)49 (D)96 (E)167

PROBLEM 14

Nina used 36 identical cubes to build a fence of cubes around a square region Part of her fence is

shown in the picture

How many more cubes will Nina need in order to fill the region inside her fence?

(A)36 (B)49 (C)64 (D)81 (E)100

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PROBLEM 15

Some square floors have been covered with white and grey tiles Floors using 4 and 9 grey tiles are

shown in the picture

Each floor has a grey tile in every corner and all the tiles around a grey tile are white How many white

tiles are needed altogether for a floor using 25 grey tiles?

(A)25 (B)39 (C)45 (D)56 (E)72

PROBLEM 16

Paul wanted to multiply an integer by 301, but he forgot the zero and multiplied by 31 instead The

result he got was 372 (He did manage to multiply by 31 correctly!) What result was he supposed to

get?

(A)3010 (B)3612 (C)3702 (D)3720 (E)30 720

PROBLEM 17

In three games FC Barcelona scored three goals and let one goal in In these three games, the club won

one game, drew one game and lost one game What was the score in the game FC Barcelona won?

(A) 2-0 (B) 3-0 (C) 1-0 (D) 4-1 (E) 0-1

PROBLEM 18

We are given three points on a sheet of paper The points are the vertices of a triangle We want to

draw another point so that the four points are the vertices of a parallelogram How many possibilities

are there for the fourth point?

(A)1 (B)2 (C)3 (D)4 (E)It depends on

the initial triangle

PROBLEM 19

The picture shows eight marked points connected by lines

One of the numbers 1, 2, 3 or 4 is to be written at each of the marked points so that the two

numbers at the ends of every line are different Three numbers have already been written

How many times does 4 appear in the completed picture?

(A)1 (B)2 (C)3 (D)4 (E) 5

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There are 10 pupils in a dance class Their teacher has 80 jelly beans After she gives the same number

of jelly beans to each of the girls in the class, there are 3 jelly beans left over How many boys are there

in the class?

(A) 1 (B) 2 (C) 3 (D) 5 (E) 6

PROBLEM 22

A cat has 7 differently-coloured kittens: white; black; red; black & white; red & white; black & red; and

white, black & red How many ways are there to put 4 kittens in a basket so that every pair in the

basket has at least one colour in common?

(A)1 (B)3 (C)4 (D)6 (E)7

PROBLEM 23

The picture shows four identical right-angled triangles inside a rectangle

What is the total area of all four triangles?

(A)46 cm2 (B)52 cm2 (C)54 cm2 (D)56 cm2 (E)64 cm2

PROBLEM 24

Alex says Pelle is lying Pelle says Mark is lying Mark says Pelle is lying Tony says Alex is

lying How many of these four boys are lying?

(A)0 (B)1 (C)2 (D)3 (E)4

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PROBLEM 25

Lina has fixed two shapes on a 5 × 5 board, as shown in the picture

Which of the following 5 shapes should she place on the empty part of the board so that none of the

remaining 4 shapes will fit in the empty space that is left? (The shapes may be rotated or turned over,

but can only be placed so that they cover complete squares.)

(A) (B)

(C)

(D) (E)

PROBLEM 26

The picture shows three identical dice stacked on top of each other

For each die, the total number of pips on every pair of opposite faces is 7 The stack was made so that

the sum of the pips on every pair of faces that meet is 5 How many pips are on the face marked X?

(A)2 (B)3 (C)4 (D)5 (E)6

PROBLEM 27

I want to draw four circles on the blackboard so that every pair of circles has exactly one common

point What is the greatest number of points that can belong to more than one circle?

(A)1 (B)4 (C)5 (D)6 (E)8

PROBLEM 28

In a particular month there were 5 Saturdays and 5 Sundays, but only 4 Fridays and 4 Mondays In the

next month there were

(A)5 Wednesdays (B)5 Thursdays (C)5 Fridays

(D)5 Saturdays (E)5 Sundays

PROBLEM 29

You are given four positive numbers , , and in ascending order of size You are asked to increase

one of them by 1 in such a way that the product of the four resulting numbers is as small as possible

Which number should you increase?

(A) (B) (C) (D) (E) either or

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PROBLEM 30

The digits of a positive five-digit number are 1, 2, 3, 4, 5 in some order The first digit of the number is

divisible by 1, the first two digits (in order) form a number divisible by 2, the first three digits (in

order) form a number divisible by 3, the first four digits (in order) form a number divisible by 4, and

the whole number is divisible by 5 How many such numbers are there?

(A) 0 (B)1 (C)2 (D)5 (E)10

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International Kangaroo Mathematics Contest 2012 – Benjamin

Level Benjamin (Class 5 & 6)Time Allowed : 3 hoursSECTION ONE - (3 points problems)

1 Basil wants to paint the slogan VIVAT KANGAROO on a wall He wants different letters

to be coloured differently, and the same letters to be coloured identically How many colours

will he need?

2 A blackboard is 6 m wide The width of the middle part is 3 m The two other parts have

equal width How wide is the right-hand part?

6 m

3 Sally can put 4 coins in a square built with 4 matches (see picture) At least how many

matches will she need in order to build a square containing 16 coins that do not overlap?

kangaroo

4 In a plane, the rows are numbered from 1 to 25, but there is no row number 13 Row

number 15 has only 4 passenger seats, all the rest have 6 passenger seats How many seats for

passengers are there in the plane?

5 When it is 4 o’clock in the afternoon in London, it is 5 o’clock in the afternoon in Madrid

and it is 8 o’clock in the morning on the same day in San Francisco Ann went to bed in San

Francisco at 9 o’clock yesterday evening What was the time in Madrid at that moment?

(A) 6 o’clock yesterday morning (B) 6 o’clock yesterday evening

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(C) 12 o’clock yesterday afternoon (D) 12 o’clock midnight

(E) 6 o’clock this morning

6 The picture shows a pattern of hexagons We draw a new pattern by connecting all the

midpoints of any neighbouring hexagons

What pattern do we get?

7 To the number 6 we add 3 Then we multiply the result by 2 and then we add 1 Then

the final result will be the same as the result of the computation

(A) (6 + 3 · 2) + 1 (B) 6 + 3 · 2 + 1 (C) (6 + 3) · (2 + 1)

(D) (6 + 3) · 2 + 1 (E) 6 + 3 · (2 + 1)

8 The upper coin is rotated without slipping around the fixed lower coin to a position shown

on the picture Which is the resulting relative position of kangaroos?

9 One balloon can lift a basket containing items weighing at most 80 kg Two such balloons

can lift the same basket containing items weighing at most 180 kg What is the weight of the

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basket?

10 Vivien and Mike were given some apples and pears by their grandmother They had 25

pieces of fruit in their basket altogether On the way home Vivien ate 1 apple and 3 pears,

and Mike ate 3 apples and 2 pears At home they found out that they brought home the same

number of pears as apples How many pears were they given by their grandmother?

SECTION TWO - (4 points problems)

11 Which three of the numbered puzzle pieces should you add to the picture to complete the

square?

12 Lisa has 8 dice with the letters A, B, C and D, the same letter on all sides of each die

She builds a block with them

B C A

Two adjacent dice always have different letters What letter is on the die that cannot be

seen on the picture?

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13 There are five cities in Wonderland Each pair of cities is connected by one road, either

visible or invisible On the map of Wonderland, there are only seven visible roads, as shown

Alice has magical glasses: when she looks at the map through these glasses she only sees

the roads that are otherwise invisible How many invisible roads can she see?

14 The positive integers have been coloured red, blue or green: 1 is red, 2 is blue, 3 is green,

4 is red, 5 is blue, 6 is green, and so on Renate calculates the sum of a red number and a blue

number What colour can the resulting number be?

15 The perimeter of the figure below, built up of identical squares, is equal to 42 cm What

is the area of the figure?

16 Look at the pictures Both shapes are formed from the same five pieces The rectangle

measures 5 cm × 10 cm, and the other parts are quarters of two different circles The difference

between the perimeter lengths of the two shapes is

17 Place the numbers from 1 to 7 in the circles, so that the sum of the numbers on each of

the indicated lines of three circles is the same What is the number at the top of the triangle?

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18 A rubber ball falls vertically through a height of 10 m from the roof of a house After

each impact on the ground it bounces back up to 4

5 of the previous height How many timeswill the ball appear in front of a rectangular window whose bottom edge has a height of 5 m

and whose top edge has a height of 6 m?

19 There are 4 gearwheels on fixed axles next to each other, as shown The first one

has 30 gears, the second one 15, the third one 60 and the last one 10 How many

rev-olutions does the last gearwheel make, when the first one turns through one revolution?

20 A regular octagon is folded in half exactly three times until a triangle is obtained, as

shown

Then the apex is cut off at right angles, as shown in the picture

If the paper is unfolded what will it look like?

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CLB EMATH

International Kangaroo Mathematics Contest 2012 – BenjaminSECTION THREE - (5 points problems)

21 Winnie’s vinegar-wine-water marinade contains vinegar and wine in the ratio 1 to 2, and

wine and water in the ratio 3 to 1 Which of the following statements is true?

(A) There is more vinegar than wine

(B) There is more wine than vinegar and water together

(C) There is more vinegar than wine and water together

(D) There is more water than vinegar and wine together

(E) There is less vinegar than either water or wine

22 Kangaroos Hip and Hop play jumping by hopping over a stone, then landing across so

that the stone is in the middle of the segment traveled during each jump Picture 1 shows how

Hop jumped three times hopping over stones marked 1, 2 and 3 Hip has the configuration of

stones marked 1, 2 and 3 (to jump over in this order), but starts in a different place as shown

on Picture 2 Which of the points A, B, C, D or E is his landing point?

A

23 There were twelve children at a birthday party Each child was either 6, 7, 8, 9 or 10

years old, with at least one child of each age Four of them were 6 years old In the group the

most common age was 8 years old What was the average age of the twelve children?

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CLB EMATH

24 Rectangle ABCD is cut into four smaller rectangles, as shown in the figure The four

smaller rectangles have the properties: (a) the perimeters of three of them are 11, 16 and 19;

(b) the perimeter of the fourth is neither the biggest nor the smallest of the four What is the

CD

25 Kanga wants to arrange the twelve numbers from 1 to 12 in a circle such that any

neighbouring numbers always differ by either 1 or 2 Which of the following pairs of numbers

have to be neighbours?

(A) 5 and 6 (B) 10 and 9 (C) 6 and 7 (D) 8 and 10 (E) 4 and 3

26 Peter wants to cut a rectangle of size 6 × 7 into squares with integer sides What is the

minimal number of squares he can get?

27 Some cells of the square table of size 4 × 4 were colored red The number of red cells

in each row was indicated at the end of it, and the number of red cells in each column was

indicated at the bottom of it Then the red colour was eliminated Which of the following

tables can be the result?

(A)

4211

0 3 3 2 (B)

1213

2 2 3 1 (C)

3300

1 3 1 1 (D)

2122

2 1 2 2 (E)

0331

0 3 1 3

28 A square-shaped piece of paper has area 64 cm2 The square is folded twice as shown in

the picture What is the sum of the areas of the shaded rectangles?

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CLB EMATH

29 Abid’s house number has 3 digits Removing the first digit of Abid’s house number, you

obtain the house number of Ben Removing the first digit of Ben’s house number, you get the

house number of Chiara Adding the house numbers of Abid, Ben and Chiara gives 912 What

is the second digit of Abid’s house number?

30 I give Ann and Bill two consecutive positive integers (for instance Ann 7 and Bill 6)

They know their numbers are consecutive, they know their own number, but they do not know

the number I gave to the other one Then I heard the following discussion: Ann said to Bill:

”I don’t know your number” Bill said to Ann: ”I don’t know your number” Then Ann said

to Bill: ”Now I know your number! It is a divisor of 20.” What is Ann’s number?

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CLB EMATH

KSF 2013 – finalized problems Benjamin

(picture 1) However, Nathalie ran out of small cubes and built only the part of the cube, as you can

see in the picture 2 How many small cubes must be added to fig 2 to form fig 1?

# 3 Find the distance which Mara covers to get to her friend Bunica

# 4 Nick is learning to drive He knows how to turn right but cannot turn left What is the smallest

number of turns he must make in order to get from A to B, starting in the direction of the arrow?

A B

# 5 The sum of the ages of Ann, Bob and Chris is 31 years What will the sum of their ages be in

three years time?

1

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