IKMC 2021 - Grades 5-6 - Self-study

Question 1

Which solid can be made with these six bricks?

Question 2

In how many places are two children holding each other with their left hands?

1. 1
2. 2
3. 3
4. 4
5. 5

Question 3

The square contains digits 1 to 9. Start at the star, follow a line and write the digits passed. The example gives 42685. Which line gives the largest number?

Question 4

Sofie writes KENGU, taking one letter from each box. Which letter must she take from box 4?

1. K
2. E
3. N
4. G
5. U

Question 5

The five pieces fit into a rectangle with a calculation on it. What is its value?

1. 22
2. 32
3. 41
4. 122
5. 203

Question 6

A measuring tape is wound around a cylinder. What number belongs at the question mark?

1. 53
2. 60
3. 69
4. 77
5. 81

Question 7

The five pieces can move only in the directions of the arrows. Which can leave through gate G?

1. A
2. B
3. C
4. D
5. E

Question 8

1. 1 part green + 3 parts white
2. 2 parts green + 6 parts white
3. 3 parts green + 9 parts white
4. 4 parts green + 12 parts white
5. All equally dark

Question 9

Mary folds a sheet exactly in half and then exactly in half again, obtaining the shown triangle. Which original shapes P, Q, R are possible?

1. Only P
2. Only Q
3. Only R
4. Only P or Q
5. Any of P, Q or R

Question 10

Question 11

1. 3244
2. 3444
3. 5172
4. 5217
5. 5444

Question 12

The map shows stations A, B, C. Tours A–Zoo–Port–A, B–Park–Zoo–B, C–Port–Park–C have lengths 10, 12, 13 km. The Zoo–Park–Port–Zoo tour is 15 km. How long is the shortest A–B–C–A tour?

1. 18 km
2. 20 km
3. 25 km
4. 35 km
5. 50 km

Question 13

Rosa follows the line from one arrow to the other. Which piece cannot be placed in the middle to make this possible?

Question 14

Each hexagon has vertex numbers summing to 30. Some numbers are hidden. What number is at the question mark?

1. 3
2. 4
3. 5
4. 6
5. 7

Question 15

Three rectangles have equal heights and the shown areas in square centimetres. AB=6 cm. What is CD?

1. 7 cm
2. 7.5 cm
3. 8 cm
4. 8.2 cm
5. 8.5 cm

Question 16

A triangular pyramid is made of ten balls, two each marked A, B, C, D, E. Three side views are shown. What letter is on the question-mark ball?

1. A
2. B
3. C
4. D
5. E

Question 17

Question 18

Each pirate tells the truth about exactly one of the two quantities, coins and diamonds, and lies about the other. Their statements are shown. What is the total number of coins and diamonds?



Pirate 1: 8 coins and 6 diamonds. Pirate 2: 7 coins and 4 diamonds. Pirate 3: 7 coins and 7 diamonds.

1. 11
2. 12
3. 13
4. 14
5. 15

Question 19

1. Carl gets at least one pear
2. Carl gets equally many apples and pears
3. Carl gets as many pears as Luca
4. Carl gets as many pears as Luca gets apples
5. Carl gets as many apples as Luca

Question 20