Problem 1

Four intersecting paths pass through the yard (see plan). Plant four apple trees so that there are equal number of apple trees on either side of each path.

Problem 2

Anna uses 32 small grey squares to frame a 7 cm by 7 cm big picture. How many small grey squares does she have to use to frame a 10 cm by 10 cm big picture?

Problem 3

Six paper strips are used to weave a pattern (see diagram).

What do you see when you look at the pattern from behind?

Problem 4

All dogs are equally heavy.

How much could one dog weigh?

Problem 5

The Kangaroo Hotel has 30 floors numbered from 1 to 30 and each floor has 20 rooms numbered from 1 to 20 . The code to enter the room is formed by joining the floor number with the room number, in that order. But this code can be confusing, as shown in the picture. Note that the code 101 is not confusing, as it can only refer to floor 10 and room 1 and never to floor 1 and room 1 , as it has the code 11 . How many codes are confusing, including the one in the figure?

Problem 6

Whenever the kangaroo goes up seven steps, the rabbit goes down three steps. When the kangaroo is on step number 56, on which step will the rabbit be?

Problem 7

Ahmed and Sara move from point A in the direction shown with the same speed. Ahmed walks around the square garden and Sara walks around the rectangular garden. How many rounds does Ahmed have to walk to meet Sara in point A again for the first time?

Problem 8

The big cube is made up of three different kinds of building blocks (see diagram). How many of the little white cubes are needed for this big cube?

Problem 9

Jan sends five postcards to his friends during his holiday.

The card for Michael does not have ducks.
The card for Clara shows the sun.
The card for Paula shows exactly two animals.
The card for Lexi shows a dog.
The card for Heidi shows kangaroos.
Which card does Jan send to Michael?

Problem 10

On the right you can see a picture of ladybird Sophie. Sophie turns.

Which of the pictures below is not Sophie?