IKMC 2027 - Grades 3-4 - Self-study SET 16 - Thematic Batch 3

A castle is built from unit cubes as shown. Anna’s top view is also shown. How many cubes are used?

A regular octagon is folded three times as shown until a triangular packet is obtained. The top corner is then cut off along the shown straight line. Which shape appears when the paper is opened?

The source gives these two calculations:
123456789 × 9 = 111111111; 123456789 × 18 = 222222222
What is 12345678 × 36?

Editorial task: calculate the expression exactly as printed, check the two supplied equalities, and explain whether any original option can be justified.



Original source options (retained):
(A) 111111111; (B) 333333333; (C) 123456789; (D) 363636363; (E) 444444444

Editorial format note: this essay examines the source wording and its assumptions. The original choices are retained for comparison.

What number belongs in the cloud containing the question mark?

Peter buys a carpet 60 dm long and 36 dm wide, decorated with alternating sun and moon squares as shown. How many moon pictures are on the whole carpet?

Which answer piece can be joined to the given piece to make a rectangle?

Alex fills the diagram with the numbers 1 through 7, using each once, so that all operations are correct. Which number can go in the question-mark box?

Lan has four differently coloured pencils and wants to colour the three countries in the map. Countries sharing a boundary must have different colours. How many colourings are possible?

Tim, Tom and Jim are triplets. Their older brother Paul is exactly three years older. Which listed number could be the sum of the four brothers’ ages?

How many three-digit numbers have both their hundreds digit and their units digit larger than their tens digit?

John has a 6-by-11 cm chocolate bar. He eats part of it, leaving the shape shown. What is the remaining area in square centimetres?

A die stands on the square grid as shown. It is rolled along the arrows. How many dots are on top when it reaches the starred square?

Which answer bracelet is the same as the six-bead bracelet shown?

Zoe has two cards, with one number written on each side. The two numbers on the first card have the same sum as the two on the second. All four numbers sum to 32. The visible numbers are 5 and 12. What are the two hidden numbers?

Twelve children stand in horizontal rows as shown. Nam can see the greatest number of other children. He is second from the left in his row and can see Hoa. Which labelled child is Nam? Each child sees only children in other rows in the direction they face.

A 90-minute film starts at 17:10. Two advertisements lasting 8 and 5 minutes are shown during it. At what time does the screening end?

The road from city A to city B is shown. Because the section A′B′ is closed, travellers follow the dashed rectangular detour. How much longer is the new route, in kilometres?

In a magical city, every ostrich wears one hat and two shoes, while every camel wears one hat and four shoes. There are 56 shoes and 16 hats altogether. How many ostriches live there?

Two gears mesh as shown. The larger has 16 teeth and the smaller 12. When the large gear makes three full turns, how many turns does the small gear make?

Alice arrives 25 minutes late. Jule arrives exactly on time at 15:45. Quentin arrives 15 minutes before Alice. When does Quentin arrive?