IKMC 2024 - Grades 7-8 - Self-study

The diagram on the right is made up of five-sided tiles of equal size. Which tile can be inserted in the missing spot so that two closed lines are formed?

What is the value of $\frac{20\times24}{2\times0+2\times4}$?

Which figure shown below cannot be formed from the rope shown on the right without cutting?

Julio cuts off four corners of a regular tetrahedron. How many corners does the object now have?

A square has a perimeter of 32 cm. The square is cut into 4 equal strips (see diagram). What is the perimeter of one such strip?

Ria has three cards with the numbers 1, 5 and 11. She wants to place the cards next to each other to form a 4-digit number. How many different 4-digit numbers can she form?

Manuel has a round transparent piece of paper with some circles (see diagram on the right). He folds it along the dashed line. What does it look like once it has been folded?

There are five different kinds of fruit in a bowl: apples, grapes, cherries, strawberries and bananas. Anna likes apples, cherries, strawberries and bananas. Berta likes apples. Conny likes grapes, cherries, strawberries and bananas. Doris likes apples, grapes and cherries. Eva likes apples and cherries. The fruits are shared out so that each person gets a different kind of fruit but everybody gets a kind of fruit that they like. Who gets the cherries?

50 children are sitting in a circle. They throw a ball. Each child that gets the ball, throws the ball to the child sitting six places to their left. Frida gets the ball 100 times during the game. How many children never get the ball during this time?

The diagram shows a rhombus. Its area is increased by adding two right-angled triangles as shown. We know that $\angle NMA=\angle BMN=90^\circ$. By what percentage does this increase the area?

Carina has baked a cake and cut it into 10 equal pieces. She ate one piece of cake and rearranged the remaining pieces evenly (see diagram). How big is the angle between two neighbouring pieces?

Four different positive whole numbers are written into the grid and are then covered up. The products of the two numbers in each row or column, respectively, are stated next to or below the grid. What is the sum of the four covered numbers?

Uli can buy exactly 12 packages of jelly babies or exactly 20 chocolate bars with her pocket money. Uli buys 9 packages of jelly babies. How many chocolate bars can she buy with the remaining money?

Which of the shapes shown on the right can you put together to form a cuboid?

All trolleys in a shop are the same. Four trolleys slid together have a total length of 108 cm (see diagram). Ten trolleys slid together have a total length of 168 cm. How long is one trolley?

Johann has several light and dark cubes. He used them to form the solid shown on the right. He made it by gluing a light cube on each side of a dark cube. Now he wants to glue on dark cubes so that no light areas can be seen from the outside. What is the minimum number of dark cubes that he will need?

The digits 0 - 9 can be drawn using horizontal and vertical lines as shown. Greg chooses two digits. Together, his digits have 1 horizontal line and 5 vertical lines. What is the sum of his two digits?

The diagram shows three semi-circles inside a rectangle. The semi-circle in the middle touches the other two semi-circles, which each touch a short side of the rectangle. The biggest semi-circle also touches the upper long side of the rectangle. The shortest distances from that side of the rectangle to the two other semi-circles are 5 cm and 7 cm, respectively (see diagram). How big is the perimeter of the rectangle in cm?

Daniel forms a $4\times4$ square from the three pieces shown and another piece. The sum of the four numbers in every row and every column is the same. What does the fourth piece look like?

Every day, penguin Paula catches 12 fish for her two children. Every day she gives one of her children 7 fish and the other 5 fish. After several days, one of her children has received 44 fish. How many fish did the other child receive?