IKMC 2027 - Grades 5-6 - Self-study SET 13 - Thematic Batch 3

Alice lists positive integers in the order shown. Which of the following numbers cannot occur in the upper-right corner of a square grid she completes in this way?

The diagram shows eight marked points joined by segments. Alice assigns each point one of 1, 2, 3, 4 so that joined points always receive different numbers. Three values are already shown. How many 4s will she use?

Fifty boys and thirty-four girls hold hands in a large circle. Exactly twenty boys hold a girl’s hand with their right hand. How many boys hold a girl’s hand with their left hand?

The illustrated word HODI has a horizontal line of symmetry. Which other listed word has the same property?



Use idealized block letters; the two lobes of B are equal.

Nine cars approach a crossroads as shown. Each will go straight, turn right or turn left; no car makes a U-turn. Their indicators are already on wherever needed. Which option shows the cars on their outgoing roads after passing the junction?



The solution checks every visible indicator and explicitly corrects the source key.

An equilateral triangle consists of 36 congruent small equilateral triangles as shown. Each small triangle has area 2. Find the area of triangle ABC.

A rectangle is divided into ten squares as shown. The shaded square has perimeter 48 cm. What is the rectangle’s perimeter?

Some natural numbers are sums of three consecutive natural numbers, for example 9=2+3+4 and 21=6+7+8. Among the first 1000 natural numbers, how many have such a representation?



Source convention: 0 is a natural number and may be a summand.

Mark must meet Alice outside a cinema at 4 p.m. He needs 5 minutes to walk to the bus stop, 19 minutes on the bus, and another 4 minutes to walk to the cinema. Buses pass his stop every 15 minutes starting at 3 p.m. What is the latest time he can leave home and arrive on time?



“On time” means arriving no later than the meeting time.

Julia’s ten circular discs form the triangular arrangement on the left. She wants to move some discs to obtain the arrangement on the right without changing her viewing direction. What is the minimum number of discs she must move?



The target has the pictured orientation but no fixed position; translating it is allowed. The source key is corrected in the solution.

On an ordinary die, the numbers of dots on opposite faces add to 7. Which pictured die could satisfy this condition?

Tommy places the pictured dominoes in a 4×4 board so that all row and column dot totals are equal. How many dots are on the hidden domino half?

All pupils of Xuân Mai A Primary School line up for exercise. Rows of 20, 25 or 30 each leave 15 pupils over; rows of 41 leave none. There are at most 1000 pupils. How many are there?

The pictured figure consists of three joined squares. The smallest square has perimeter 24 cm. What is the perimeter of the whole figure?

The class makes barriers from strings bearing small rings in the repeating pattern shown. Each barrier has 2002 strings. How many rings are attached to each barrier?

A fox tells the truth on Sunday, Monday, Tuesday, Wednesday and lies on the other days. A wolf tells the truth on Thursday, Friday, Saturday, Sunday and lies on the other days. One day they both say, “Yesterday was a day on which I lied.” What day is it?

How many trailing zeros does n=3×6×9×12×15×18×⋯×99 have?

A river divides a town into two banks, with two islands and the pictured bridges. How many routes start at A, end at B, and cross every bridge exactly once?



Use the arrows as the required entry bridge from A and exit bridge to B, as intended by the source.

Five runners compete. Adam is slower than Martin but faster than Susan. Lucy finishes before Adam and Martin. Biba is faster than Martin but slower than Lucy. Who finishes third?

A penguin starts with 18 on a calculator and performs exactly 100 operations, each multiplying or dividing by 2 or 3 whenever possible. Which listed result is impossible?