IKMC 2024 - Grades 5-6 - Set 2 - Self-study

Alina folds the picture along the dashed line. Which of the following squares folds onto an identical square?

The picture shows the first squares of a hopping game. The pictures repeat every four squares. In which listed square will Mia land only on her right foot?

Reading note: start at the bottom square and move upwards, as the footprints indicate.

Sasha created a secret alphabet. The picture gives his codes for “basil” and “red”, in that order. How does he write “bread”?

Which strip should fill the gap so that each child is connected to a different kite? Crossings of strings are not junctions.

Dina places three bricks on the floor behind a wall. The picture shows the view from the front. How do the bricks look from the back?

Mona draws the three-segment figure without lifting her pencil. The segment lengths are 3 cm, 2 cm and 1 cm. What is the shortest total distance she can draw?

Two wheels, each marked with seven positions, turn in opposite directions. Each makes one complete turn in seven minutes. At each whole minute, every letter aligns with a number. Initially A aligns with 1, B with 2, and so on. When C aligns with 2, which number aligns with F?

Six boxes are stacked on a truck as shown. A worker takes one box at a time only when no other box is on it, and immediately places it on the ground or on a box already removed. Which final arrangement cannot be built?

Pieter has a 445 g package and weights of 500, 200, 200, 100, 50, 20, 20 and 5 grams. Weights may be placed on either pan. What is the minimum number of weights needed to balance the package?

Hotel rooms are numbered consecutively from 1 with no omissions. The digit 2 appears fourteen times and the digit 5 three times in the room numbers. What is the largest possible number of rooms?

Two identical rectangles, each of area 18, overlap to form the new rectangle shown. The new rectangle consists of three identical squares. What is its area?

Five chocolate boxes A, B, C, D and E originally contain flavours numbered 1–5, 2–6, 3–7, 4–8 and 5–9 respectively. After most chocolates are eaten, one remains in each box, as shown. What is the label of box X, containing flavour 5?

Rosa draws the arrangement of identical rectangles shown. Its total width is 45 cm and its total height is 30 cm. What is the area of one rectangle?

There are numbers in sixteen circles around a ring. Numbers in neighbouring circles differ by 1. One circle contains 5 and another contains 13. How many different numbers appear?

The two large squares have equal area. In the first, adjacent side midpoints are joined and the four corner regions are shaded. In the second, four small squares, each with side one third of the large square’s side, are shaded. If the first shaded area is 9, what is the second shaded area?

The diagram shows the Braille patterns for digits 0 to 9. How many two-digit numbers use exactly five black dots altogether?

Some of the sixteen hexagonal cells contain honey. The number in a cell tells how many neighbouring cells contain honey; neighbours share a full edge. How many cells contain honey?

Annie places the numbers 1 to 10 in the ten circles, once each. The sum on each straight line of four circles must be 23. What number belongs in the circle marked “?”?

Christian cuts squares of side lengths 1, 2, 3 and 6 from the four corners of a large square. The remaining area is half the original area. What is the perimeter of the remaining shape?

Ria fills the grid with 1, 2, 3 and 4 so that each row and column contains each number exactly once. Every inequality shown must be true; the pointed end faces the smaller number. What number must go in the grey circle?