IKMC 2017 — Grades 5–6

Four cards lie in a row.



Which row of cards can you not obtain if you can only swap two cards?

A fly has 6 legs, a spider has 8. Together, 3 flies and 2 spiders have as many legs as 9 chickens and...

Alice has 4 pieces of this shape .

Which picture can she not make from these 4 pieces?

Kalle knows that $1111\times1111=1234321$. Then $1111\times2222=?$

On a planet there are 10 islands and 12 bridges. All bridges are open for traffic right now.



What is the smallest number of bridges that must be closed in order to stop the traffic between A and B?

Jane, Kate and Lynn go for a walk. Jane walks up front, Kate walks in the middle and Lynn walks behind. Jane weighs 500 kg more than Kate. Kate weighs 1000 kg less than Lynn. Which of the following pictures shows Jane, Kate and Lynn in the right order?

A special die has a number on each face. The sums of the numbers on opposite faces are all equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth face?

Martin wants to colour the squares of the rectangle below so that one third of the squares are blue and half of them are yellow. The rest of the squares are to be coloured in red.



How many squares will he colour in red?

During the time it took Peter to solve 2 problems of the “Kangaroo” contest, Nick managed to solve 3 problems. Together, the boys solved 30 problems. How many problems did Nick solve more than Peter?

Bob folded a piece of paper, used a hole puncher and punched exactly one whole in the folded paper. The unfolded piece of paper can be seen in the picture:



Which of the following pictures shows the lines along which Bob folded the piece of paper?

The Modern Furniture store is selling sofas, loveseats, and chairs made from identical modular pieces as shown in the picture. Including the armrests, the width of the sofa is 220 cm and the width of the loveseat is 160 cm.



What is the width of the chair?

The 5 keys fit the 5 padlocks. The number on each key refers to the letters on the matching padlock.



What is written on the last key?

Tom writes all the numbers from 1 to 20 in a row and obtains the 31-digit number: 1234567891011121314151617181920.

Then he deletes 24 of the 31 digits so that the remaining number is as large as possible. Which number does he get?

Morten wants to put the block below into a rectangular box.



Which of the following is the dimensions of the smallest fitting box?

When we add the numbers in each row or each column, we get the results shown next to the board.



Which statement is true?

Editable table:

| | Column 1 | Column 2 | Row sum |
|---|---|---|---|
| Row 1 | $a$ | $b$ | 2 |
| Row 2 | $c$ | $d$ | 3 |
| Column sum | 1 | 4 | |

Peter went hiking in the mountains for 5 days. He started on Monday and his last trip was on Friday. Each day he walked 2 km more than the day before. When the tour was over, his total distance was 70 km. What distance did Peter walk on Thursday, in km?

There is a picture of a kangaroo in the leftmost triangle. The dashed lines act as mirrors. The first 2 reflections are shown.



What does the reflection look like in the shaded triangle?

Rafael has three squares. The first one has side length 2 cm. The second square has side length 4 cm and one of its vertices is placed at the centre of the first square. The last square has side length 6 cm and one of its vertices is placed at the centre of the second square, as shown in the picture. (All the angles are right angles).



What is the area of the figure, in $\text{cm}^2$?

Boris has an amount of money and 3 magic wands that he can use only once.



In which order must he use these wands to obtain the largest amount of money?

| Wand | Effect |
|---|---|
| $+1$ | Adds 1 EUR |
| $-1$ | Subtracts 1 EUR |
| $\times2$ | Doubles the amount |

Four players scored goals in a handball match. Each of them scored a different number of goals. Of the four, Mike was the one who scored the least number of goals. The other three scored 20 goals among them. What is the largest number of goals Mike could have scored?