IKMC 2017 — Grades 3–4

Which of the pieces (A)–(E) will fit between the two pieces below so that the two equalities are fulfilled?

John looks through the window. He sees half of the kangaroos in the park (see picture). How many kangaroos are there in the park?

Two gridded transparent sheets are darkened in some squares, as shown. They are both put on top of the board shown in the middle. Then the pictures behind the darkened squares cannot be seen. Only one of the pictures can still be seen, which one is it?



Editable picture-board transcription:

| Left | Middle | Right |
| --- | --- | --- |
| Star | Butterfly | Car |
| Basketball | Dog | Cup |
| Flower | Bird | Clock |

Left transparent sheet:

| Left | Middle | Right |
| --- | --- | --- |
| Dark | Clear | Dark |
| Clear | Dark | Clear |
| Dark | Clear | Dark |

Right transparent sheet:

| Left | Middle | Right |
| --- | --- | --- |
| Dark | Clear | Dark |
| Dark | Clear | Dark |
| Clear | Dark | Clear |

A picture of footprints was rotated. Which footprints are missing?

What number is hidden behind the bear?

In the tables, correct sums are shown. What number is in the box with the question mark?

| + | 11 | 7 | 2 |
| --- | --- | --- | --- |
| 6 | 17 | 13 | 8 |
| Hidden | Hidden | ? | 11 |

Dolly accidentally broke the mirror into pieces. How many pieces have exactly four sides?

In the figure we see a necklace of six beads.

Which one is the same necklace?

The picture shows the front of Ann’s house. The rear of her house has three windows and no door. What view does Ann see when she looks at the rear of her house?

Which one is true?

Balloons are sold in packets of 5, 10 and 25. Marius buys exactly 70 balloons. What is the smallest number of packets he could buy?

Bob folded a piece of paper. He cut exactly one hole in the paper. Then he unfolded the piece of paper and saw the result as shown in the picture.

How had Bob folded his piece of paper?

There is a tournament at the pool. First 13 children signed up and then another 19 signed up. Six teams with an equal number of members are needed for the tournament. At least how many more children need to sign up so that the six teams can be formed?

Numbers are placed in the cells of the $4\times4$ square shown in the picture.

| Column 1 | Column 2 | Column 3 | Column 4 |
| --- | --- | --- | --- |
| 1 | 2 | 1 | 3 |
| 4 | 1 | 1 | 2 |
| 1 | 7 | 3 | 2 |
| 2 | 1 | 3 | 1 |

Mary finds the $2\times2$ square where the sum of the numbers in the four cells is the largest. What is that sum?

David wants to cook 5 dishes on a stove with only 2 burners. The times needed to cook the 5 dishes are 40 min, 15 min, 35 min, 10 min and 45 min. What is the shortest total time in which he can cook the 5 dishes? (He may only remove a dish from the stove when it is cooked.)

Which number should be written in the circle containing the question mark?

The picture shows a group of building blocks and a plan of the same group. Some ink has dripped onto the plan. What is the sum of the numbers under the ink blots?



Editable plan transcription (— means outside the plan):

| Column 1 | Column 2 | Column 3 | Column 4 |
| --- | --- | --- | --- |
| — | — | Ink | — |
| 3 | Ink | 4 | 1 |
| — | 1 | — | — |
| — | 1 | 3 | — |
| — | — | 1 | — |

How long is the train?

George starts training at five in the afternoon. It takes him 5 minutes to go from his house to the bus stop. The bus ride is 15 minutes long. It takes him 5 minutes to go from the bus stop to the field. The bus runs every 10 minutes, starting at six in the morning. At what time at the latest does he have to leave his house to arrive at the field on time?

A small zoo has a giraffe, an elephant, a lion and a turtle. Susan wants to plan a tour where she sees 2 different animals. She does not want to start with the lion. How many different tours can she plan?