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IKMC 2010 — Grades 3–4

Question 1

In the picture below, you see a map. In the middle, a piece is missing. The cat should be able to reach the milk, and the mouse should be able to reach the cheese, but the cat and the mouse must not meet each other. What should the piece in the middle look like?

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Question 2

A 40 minute long lesson began at 11:50. Exactly in the middle of the lesson, a bird flew into the classroom. At what time did this happen?
  1. 11:30
  2. 12:00
  3. 12:10
  4. 12:20
  5. 12:30

Question 3

Which square contains 3 quadrilaterals, 3 circles and 4 hearts?
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Question 4

In a cafe, the soup costs €4, the main course costs €9 and the dessert costs €5. The three courses when ordered together cost €15. How many euros cheaper is this, than ordering the same three courses separately?
  1. €3
  2. €4
  3. €5
  4. €6
  5. €7

Question 5

Six coins form a triangle (see picture). What is the smallest number of coins that must be moved to create the circle on the right?

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  2. 2
  3. 3
  4. 4
  5. 5

Question 6

Four friends each eat some ice cream. Mike eats more than Franz, Jaroslav eats more than Veit and Jaroslav eats less than Franz. Put the friends in order according to how much ice cream they have eaten, starting with the largest amount.
  1. Mike, Jaroslav, Veit, Franz
  2. Veit, Mike, Franz, Jaroslav
  3. Mike, Franz, Jaroslav, Veit
  4. Jaroslav, Veit, Mike, Franz
  5. Jaroslav, Mike, Veit, Franz

Question 7

I have tiles that look like the following figure.

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Which pattern can I not create with them?
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Question 8

Eva is a centipede with exactly 100 feet. Yesterday, she bought 16 pairs of shoes and wore them straight away. Even so she still had 14 feet with no shoes. On how many feet did she already wear shoes before going shopping yesterday?
  1. 24
  2. 40
  3. 54
  4. 70
  5. 77

Question 9

Consider the equation below. Which number should replace the triangle?

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  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 10

Maria folds the square piece of paper shown below in such a way that the kangaroos exactly overlap each other. Along how many of the lines shown should she fold the paper?

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  1. 0
  2. 1
  3. 2
  4. 3
  5. 4

Question 11

Matthias and Klara live in a tower block. Klara lives 12 floors above Matthias. One day, Matthias climbs the staircase to visit Klara. When he is halfway up, he is on the 8th floor. On which floor does Klara live?
  1. 12th
  2. 14th
  3. 16th
  4. 20th
  5. 24th

Question 12

A large cube is made of 64 small cubes. The 5 visible faces of the large cube are green, the bottom face is red. How many of the small cubes have 3 green faces?

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  1. 4
  2. 8
  3. 16
  4. 20
  5. 24

Question 13

Kangi walks directly from the zoo to school and counts the flowers along the way. Which of the following numbers can he not obtain this way?

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  1. 9
  2. 10
  3. 11
  4. 12
  5. 13

Question 14

A ferry boat can transport, in one trip, either 10 cars or 6 lorries. Yesterday the boat crossed the river 5 times. It was always fully loaded and transported a total of 42 vehicles. How many of these were cars?
  1. 10
  2. 12
  3. 20
  4. 22
  5. 30

Question 15

Hans began a chain-email. He sent an email to his friend Peter, who sent it on to 2 more people. Each person that receives the email should send it to 2 more people. After 3 rounds, $1+2+4=7$ people have received the email. How many people have received the email after 5 rounds?
  1. 15
  2. 16
  3. 31
  4. 33
  5. 63

Question 16

On a playground, some children measure the length of the playground with their strides. Anni makes 15 strides, Betty 17, Denis 12 and Ivo 14. Who has the longest stride?
  1. Anni
  2. Betty
  3. Denis
  4. Ivo
  5. Not possible to answer

Question 17

Every cell of a $4\times4$ table contains a playing card (their suits are shown in the picture). One lead allows switching the positions of any two cards. At least, how many leads will be played so that each row and each column will contain all suits?

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Editable table:

| Column 1 | Column 2 | Column 3 | Column 4 |
| --- | --- | --- | --- |
| ♥ | ♥ | ♦ | ♣ |
| ♦ | ♠ | ♠ | ♥ |
| ♣ | ♦ | ♠ | ♣ |
| ♠ | ♣ | ♥ | ♦ |

♥ hearts; ♦ diamonds; ♣ clubs; ♠ spades.
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 18

The expression $60\times60\times24\times7$ calculates:
  1. The number of minutes in seven weeks.
  2. The number of hours in sixty days.
  3. The number of seconds in seven hours.
  4. The number of seconds in one week.
  5. The number of minutes in 24 weeks.

Question 19

Two years ago, the cats Tim and Tom together were 15 years old. Now Tom is 13 years old. In how many years will Tim be 9 years old?
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 20

Kamilla wrote down all of the numbers from 1 to 100 one after another in a table with 5 columns. A part of the table is shown. Her brother cut out a piece of the table and erased some of the numbers. Which of the following could be this piece?

| Column 1 | Column 2 | Column 3 | Column 4 | Column 5 |
| --- | --- | --- | --- | --- |
| 1 | 2 | 3 | 4 | 5 |
| 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 |
| 16 | 17 | 18 | 19 | 20 |

Original table illustration:

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  1. | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 |
    | --- | --- | --- | --- | --- |
    | | 43 | | | |
    | | | 48 | | |

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  2. | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 |
    | --- | --- | --- | --- | --- |
    | | | 58 | | |
    | | 52 | | | |

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  3. | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 |
    | --- | --- | --- | --- | --- |
    | | | | 69 | |
    | | 72 | | | |

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  4. | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 |
    | --- | --- | --- | --- | --- |
    | | 81 | | | |
    | | 86 | | | |

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  5. | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 |
    | --- | --- | --- | --- | --- |
    | | 90 | | | |
    | | | | 94 | |

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