IKMC 2025 - Grades 5-6 - Self-study

Which piece completes the pattern?

Anna builds a wall of black and grey bricks showing 2025. What can Bella read on the back of the wall?

A bookshelf has 17 books on top, 15 in the middle and 7 on the bottom. Monika wants equal numbers on the three shelves while moving as few books as possible. How many books must she move from the middle to the bottom?

Equal grey squares are glued onto a cube as shown. All cube faces then look the same. How many grey squares were used altogether?

Thea rotates a painted hexagon clockwise by one sector at a time. The first rotation is shown. Which hexagon appears after the eighth rotation?

Rain has erased some numbers from the burger menu. The burgers are listed in increasing price order. Which listed price appeared on the board?

Six children race. Ariadne finishes third. Bill finishes sixth, just behind Ernest. Fatima finishes between Ariadne and Ernest. Diana overtakes Charles just before the finish. Who wins?

A three-part unfolded card has numbers in the centre and holes in the left and right panels. Mike folds the right panel onto the centre and sees 2,3,5,6 through its holes. He then folds the left panel over both. What is the sum of the numbers still visible?

Three turtles race 10 km, each at constant speed. When the first finishes, the second has travelled one quarter of the distance and the third one fifth. How far is the third from the finish when the second finishes?

Vera replaces the two question-mark cubes by numbered cubes. Each number must be at least 2 greater than the number immediately below it. How many ways are possible?

Each of the five spinners is divided into equal-sized sectors, with different numbers of sectors. Anna wins when the pointer stops on a dark sector. Which spinner gives the best chance?

Which shape cannot be placed on the large board so that all its squares lie only on white squares?

Five swimmers swim the same distance in a relay, one after another without stopping. The stopwatch shows the cumulative time after each swimmer, beginning with 2 minutes 8 seconds for the first. Which swimmer is fastest?

Jana cuts four equal small squares from the corners of a square sheet. The removed area totals 16 cm² and the remaining cross has area 9 cm². What is the perimeter of the cross?

Each card contains two three-digit numbers with some hidden digits. On one card the two numbers have equal digit sums. Which card can it be?

The figure consists of equal squares. B is midway between A and C; D is midway between C and E. Maria draws a straight line from S to one of A–E to divide the figure into equal areas. Which point must she choose?

Hassan fills each cell with 0 or 1. Every row, column and the two main diagonals must sum to exactly 3. A zero is already entered. What is the sum in the question-mark cells?

A witch has 10 apples,9 bananas and 6 pears. She transforms every fruit into a different type; an apple becomes a banana or pear. Afterwards she has 15 apples,7 bananas and 3 pears. How many apples became bananas?

The square has side length 10 cm. The vertical centre line divides it into two equal rectangles. What is the grey area?

Joanna divides the figure into five congruent parts, each made of three squares. Which letter belongs to the same part as the star?