IKMC 2027 - Grades 5-6 - Self-study SET 8 - Thematic Batch 3

Choose the pieces that replace A, B, C and D, in that order, to complete the railway picture. Which sequence of piece numbers is obtained?

Ben has a pearl engraved with a kangaroo and pierced by a hollow tube through its centre. He slides it along the bent wire shown. What will the pearl look like near the other end of the wire?



Planar-sliding convention: carry the pearl around the bends without turning it over or adding an independent twist around the wire.

Alex, Bob and Carl walk together every morning. Whenever Alex does not wear a hat, Bob wears one. Whenever Bob does not wear a hat, Carl wears one. This morning Bob is not wearing a hat. Who is wearing a hat?

Julia has four differently coloured pencils. She colours every region of the island shown, using one or more of those colours. Regions sharing a boundary must have different colours. How many different colourings are possible?

How many digits does the natural number 4⁵×5¹³ have?

For a natural number n, let s(n) be the sum of its digits. For example, s(692)=6+9+2=17. What is s(s(6248))?

Jenny places the digits 0 to 9 in the ten circles shown, using each once. Any two directly connected circles must contain one even and one odd number. How many valid fillings are there?

Annie replaces the letters in KANGAROO by digits. Equal letters get equal digits and different letters get different digits. She obtains the largest possible number divisible by 9. Which digit replaces O?

A Ferris wheel has an even number of equally spaced cabins, labelled consecutively from 1. When cabin 25 is at the lowest position, cabin 8 is at the highest position. How many cabins are there?



The wheel picture is schematic; the number of drawn cabins is not the unknown total.

A cylindrical cup is 10 cm tall and contains some water. The diagrams show the water when the cup is upright and when it is tilted. What is the water depth when the cup is upright?



Diagram condition: the tilted water surface meets the highest point of the bottom rim and the lowest point of the top rim, as drawn; no water is lost.

A yard is divided into nine square cells, with one kangaroo in each as shown. At a drumbeat, every kangaroo jumps to a cell sharing an edge with its starting cell. Which statement below is true?

Twenty-five bulbs are arranged in the 5×5 array shown. Touching one bulb toggles that bulb and every bulb in its row or column. All bulbs are initially on. What is the smallest number of touches needed to turn all bulbs off?

The boomerang-shaped figure has a boundary consisting of eight semicircles, each of diameter 1 cm. What is its area?

One hundred pandas live in the mountains of Sichuan, China. Seventy-five like mushrooms and sixty like bamboo. Five like neither mushrooms nor bamboo. How many like both?

An isosceles triangle has perimeter 525 mm. Its base is half as long as either equal side. How long is each equal side, in centimetres?



Source-key correction: the printed key D is incorrect. The exact given measurements yield C,21 cm. The original choices are retained.

Peter rearranges all four digits of a four-digit natural number into two two-digit numbers. One of the resulting numbers is divisible by the other. Which listed original number could he have chosen?

The carriages of a special train in Kangcity are numbered according to the pattern shown. What number belongs on the last carriage?



Pattern convention: continue the doubling of successive increases 2,4,8,16,…

After Tom’s owner discovered which cat had stolen food, the three cats stopped stealing and tried to help her. One day she rewarded them with fish, milk, meat and cheese, and Tom invited Jerry. Tom and Butch do not choose cheese; Tom does not choose milk; Spike chooses fish. Each animal chooses a different food. What does Jerry choose?

Bob writes natural numbers in a row of eleven cells so that every three consecutive cells sum to 21. The first cell contains 7 and the ninth contains 6. What is in the second cell?

Maria and her older brother John share a birthday, which is today. When John was born, Maria’s age was one third of their mother’s age. Now Maria is half as old as their mother. Which statement about John’s present age is true?



Original source choices (retained):

A. One third of Maria’s age

B. 6 years

C. Half of Maria’s age

D. 10 years

E. None of the other four statements is correct

Source consistency task: retain and examine the original “older brother” wording. Derive the age relation, explain the contradiction, and identify the source-intended answer only after separately correcting the relationship.