IKMC 2015 - Grades 3-4 - Self-study

Follow the operations shown. Which number replaces the question mark?

Eric had 10 equal metal strips. He screwed pairs of them together into five long strips as shown. Which strip is the longest?

Which number is hidden behind the square?

Starting at 1, draw a line to every second dot around the circle until returning to 1. The first two lines are already drawn. What figure do we get?

Lucy had some kangas in her wallet as shown. She went to a shop, bought a ball and paid 7 kangas. How many kangas did she have when she left the shop?

A whole number has two digits. The product of its digits is 15. What is the sum of its digits?

The figure shows an island with a highly indented coastline and several frogs. How many frogs are sitting on the island?

My umbrella has KANGAROO written on top, as shown. Which of the pictures also shows my umbrella?

Basil wants to cut the shape in Figure 1 into identical triangles as in Figure 2. How many triangles will he get?

Luis has 7 apples and 2 bananas. He gives 2 apples to Yuri, who gives bananas to Luis in return. Luis then has as many apples as bananas. How many bananas did Yuri give him?

Jack built a cube from 27 small cubes colored black or white, as shown. No two small cubes of the same color share a face. How many white cubes did Jack use?

In a speed skating competition 10 racers reached the final. Tom overtook 3 racers more than overtook him. Which place did Tom end up in?

Editorial clarification: the intended comparison is between racers Tom finished ahead of and racers who finished ahead of Tom. The printed word “overtook” is imprecise if read as counting passing events during the race.

Josip has four toys: a car, a doll, a ball and a ship. He wants to put them in a line on a shelf. The ship must be next to the car and the doll must be next to the car. In how many ways can he arrange them?

Pete rides a bicycle in the park as shown. He starts at S in the arrow direction. At the first crossroad he turns right, at the next left, then right, then left, and continues alternating. Which sign will he not pass?

There are five ladybugs as shown. Two are friends if their numbers of spots differ by exactly 1. On Kangaroo Day each ladybug sent one SMS greeting to each friend. How many greetings were sent?

The figure is divided into three identical pieces. What did the pieces look like?

Luisa wants to fold a cube from a paper net. By mistake she drew 7 squares instead of 6. Which square must she remove so that the figure stays connected and folds into a cube?

Three transparent sheets have the patterns shown. We may rotate them but not turn them over, then put them exactly on top of each other. What is the maximum possible number of black squares seen from above?

Write 2, 3, 5, 6 and 7 in the cross so that the row sum equals the column sum. Which numbers can be written in the centre?

Peter has ten balls numbered 0 to 9. John received three, George four and Ann three. The products of their numbers are 0 for John, 72 for George and 90 for Ann. What is the sum of the numbers John received?