IKMC 2027 - Grades 5-6 - Self-study SET 11 - Thematic Batch 3

During a discussion, Alex says that Pelle was wrong to claim that Mark was lying. Mark replies that Pelle is the liar, while Tony says that Alex is lying. How many of the four have said something false?

Julia has the piece of card shown. Which of the following solids can she fold from it?

A teacher writes 1 on the board and asks Tâm to write any other natural number. Each subsequent student writes the sum of all numbers already on the board. Mai writes 72000. Which listed number could not have been Tâm’s number?

Justine has a triangular piece of card. She marks the midpoint of each side and cuts along every segment joining two of these midpoints. How many triangular pieces does she obtain?

Captain Jack sails the Black Pearl from the source to the mouth of a river in 4 days, and back upstream in 6 days. One day he takes a raft and lets it drift freely downstream. How many days does the raft take to travel the full river? The boat’s still-water speed and the current speed are constant.

In CrazyTown, the houses on the right-hand side of Green Street are numbered with positive odd integers containing no digit 3, in increasing order. If the first house is numbered 1, what is the number of the fifteenth house?

Emily first lays blue and red beads in an alternating row, with blue beads at both ends. She inserts a yellow bead between every adjacent blue-red pair, then adds one yellow bead before the first blue bead and one after the last. If she uses 10 red beads, how many yellow beads does she use?

In a ball-dropping game, a player drops a ball into the partitioned box shown. A ball that lands on a partition may roll into the neighbouring compartment on either its left or right. Of the five balls in the picture, how many could fall into compartment A?



Original source choices (retained):

A. 1

B. 2

C. 3

D. 4

E. 5

Editorial consistency task: preserve the original five-ball wording and choices, compare them with the six drawn positions, and explain the source’s conditional answer. No automatic key.

Max writes the numbers 1 to 9 once each in a 3×3 grid. The numbers 1, 2, 3 and 4 are already placed as shown. Two numbers are neighbours if their cells share a side. After filling the grid, Max finds that the neighbours of 9 sum to 14. What is the sum of the neighbours of 7?

Today is Sunday. Francis begins reading a 290-page book. He reads 4 pages every day except Sunday, when he reads 25 pages. How many more days from today will it take him to finish the book?



Original source choices (retained):

A. 5

B. 46

C. 40

D. 35

E. 41

Editorial counting task: distinguish reading days including today from calendar days after today. Explain both 41 and 40; no automatic key.

Sophie colours pictures in the repeating order blue, green, red, black, blue, green, red, black, and so on. What colour is picture number 29?

Alice is searching for a secret positive integer. Tom says it is 9; Andre says it is even; Roman says it is prime; Michael says it is 15. Exactly one of Roman and Tom is truthful, and exactly one of Michael and Andre is truthful. What is the secret number?

An exhibition centre has 25 equilateral-triangle rooms arranged as shown. Each room has a door on each of its three sides leading to a neighbouring room or outside. A visitor wants to see as many rooms as possible while passing through each room at most once. What is the maximum number of rooms the visitor can see?



Source-intended route convention: one entrance and one exit, with no leaving the building and re-entering during the visit.

Kate says that her age plus her mother’s age is 36, and her mother’s age plus her grandmother’s age is 91. How old was her grandmother when Kate was born?

Farah earns 150000 đồng for every two working days at a bakery. From the start of work, she shops for food and necessities every three days. After 90 working days, she has saved 3150000 đồng. If she spends the same amount on every shopping trip, how much does she spend per trip?



Accounting convention used by the source: these 90 working days form the counted schedule, with 30 shopping trips on days 3,6,…,90; savings are earned wages minus these purchases, with no initial balance or other income/expense.

Peter forms a rectangular block from three pieces, each consisting of four unit cubes. The picture shows two of the pieces in place. What shape is the third piece?

The internal angle bisectors of triangle ABC meet at I. Given ∠AIB=110°, ∠BIC=130° and ∠AIC=120°, what is ∠ABC?

Positive integers are written on the six faces of a cube so that all three opposite-face pairs have the same sum. Ben sees five numbers: 5, 6, 9, 11 and 14. What is written on the remaining face?

Jenny has two rectangular containers with square bases. The first has base side 10 cm and height 50 cm and is said to hold at most 1 litre. The second has twice the base side of the first but half its height. What is its maximum capacity?



Original source choices (retained):

A. 0.5 litre

B. 1 litre

C. 2 litres

D. 4 litres

E. None of the other options is correct.

Editorial consistency task: compare the stated 1 litre with the printed dimensions, retain the source’s scale-ratio argument conditionally, and explain why the literal data conflict. No automatic key.

Bin says that drawing three squares may create additional shapes where they overlap, as in the example. When three identical squares are drawn, what is the greatest total number of squares of possibly different sizes that can appear?



Original source choices (retained):

A. 3

B. 5

C. 7

D. 9

E. 11

Original maximum unresolved. Separately scored editorial exercise: verify the supplied eight-square counterexample to the source’s claim of seven. Do not claim that eight is the true maximum without an upper-bound proof.