IKMC 2027 - Grades 3-4 - Self-study SET 23 - Thematic Batch 3

Linda pins three photographs in a row using eight pins, as shown. If Peter pins seven photographs in the same way, how many pins does he need?

A digital clock displays the time shown. At how many times in one day does it use exactly these same four digits?

A round cake can be divided into two equal parts with one straight cut, and into three equal parts with three straight cuts. What is the smallest number of cuts needed to divide it into twelve equal parts?

Editorial task: state the source’s radial-sector convention (full diameter cuts, no moving or stacking), give its construction, and explain the scope of the minimum claim.



Original source options (retained):
(A) 4; (B) 6; (C) 8; (D) 10; (E) 12

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

Basil colours the letters in the slogan VIVAT KANGAROO. Different letters must have different colours, and equal letters must have the same colour. How many colours does he need?

How many three-digit numbers have digit sum exactly 4?

A stout man takes 24 ducks, each weighing 2 kg, to market. He trades every two ducks for one 4-kg Muscovy duck. Then he trades each Muscovy duck for four 1-kg chickens. Next he trades every eight chickens for one 8-kg goose. Finally he trades all the geese, every two for one 16-kg piglet. How many piglets does he take home?

Luis has seven apples and two bananas. He gives Yuri two apples and receives some bananas in return. Afterwards he has equal numbers of apples and bananas. How many bananas does Yuri give him?

In the word KANGAROO, one move swaps a pair of neighbouring letters. What is the smallest number of moves needed to bring all the vowels together? The vowels are U,E,O,A,I.

The picture shows a calendar. Unfortunately, ink has covered part of it. On which weekday does the 25 th of this month fall?

From a distance, we see the city skyline below. Which of the following shapes does not appear in that skyline?

Hern has 500 coins. He plans to buy five sports books and some pencils. Each book costs 80 coins and each pencil 30 coins. What is the greatest number of pencils he can buy?

The timetable below gives hours in a day (for example A 1 is 21:00 and B 3 is 09:00). Choose one cell in each column from left to right so that the selected times are in increasing order within the same day, with the A-column time earliest. Which option is correct?

A digital clock displays 20:07. What is the shortest elapsed time before it again displays a time using those four digits?

Editorial note: the correct wait is absent from the original options. Find the next valid display and explain the discrepancy. Manual scoring.



Original source options (retained):
(A) 4 hours 2 minutes; (B) 6 hours; (C) 10 hours 55 minutes; (D) 11 hours 13 minutes; (E) 24 hours

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

Mia adds small cubes one at a time to build a 3 × 3 × 3 cube. She takes these five pictures at different times. Which is the fourth picture?

Simona puts the digits 2, 0, 2, 5 in the boxes of □ + □ − □ + □. Which order gives the largest result?

Which rope ties into a knot when its two ends are pulled?

Larissa spins her sail. Which sail could be hers?

On a normal die, opposite faces have a total of 7 spots. Which die could be normal?

Alex steps on the tracks shown. Which pattern is hidden beneath her shoe?

Kenny jumps from School to Zoo: ↑ 2, ↖ 2, ↙ 1, ← 4, as drawn. From Zoo he then jumps → 3, ↗ 2, ↑ 2. Which house does he reach?