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IKMC 2023 - Grades 5-6 - Self-study

Question 1

Holger fills the table with the numbers up to 40, continuing the shown pattern. Which piece could he cut from the table?

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Question 2

Matchsticks form digits as shown. For example, 15 and 8 each need seven matchsticks. What is the largest positive number that can be built with seven matchsticks?

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  1. 31
  2. 51
  3. 74
  4. 711
  5. 800

Question 3

Which shape cannot be divided into two triangles by a single straight line?
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Question 4

Rosalinde folds the marked paper into a cube. Which cube can she obtain?

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Question 5

Claude climbs from the bottom to the top of the cylindrical tower. All steps have equal size. Nine steps are visible. How many are hidden?

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  1. 9
  2. 10
  3. 11
  4. 12
  5. 13

Question 6

Anna has five circular discs of different sizes. She builds a tower of four discs, each smaller than the one directly below it. How many different towers are possible?

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  1. 4
  2. 5
  3. 9
  4. 12
  5. 20

Question 7

Four tapes M, N, P and Q surround the parcel. In what order, from first to last, were they placed?

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  1. M, N, Q, P
  2. N, M, P, Q
  3. N, Q, M, P
  4. N, M, Q, P
  5. Q, N, M, P

Question 8

Alice has the four puzzle pieces shown. Which pair can be combined to form the hexagon?

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

Question 9

The grey circle with three holes is placed on the clock-face and rotated about its centre. Which three numbers can be seen at the same time?

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  1. 2, 4, 9
  2. 1, 5, 10
  3. 4, 6, 12
  4. 3, 6, 9
  5. 5, 7, 12

Question 10

Jonte glues the grey semicircle and two white quarter-circles onto the black disc. Which pattern cannot be obtained?

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Question 11

Francesca writes three consecutive two-digit numbers in increasing order, replacing digits with symbols: □◇, ♡△, ♡□. Which number comes next?
  1. □♡
  2. □□
  3. ♡♡
  4. ◇□
  5. ♡◇

Question 12

A patio uses square tiles of three sizes. The smallest squares have perimeter 80 cm. What is the length of the snake shown by the thick line?

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  1. 380 cm
  2. 400 cm
  3. 420 cm
  4. 440 cm
  5. 1680 cm

Question 13

The picture is the mirror image of a digital clock behind me. Which image will I see in the mirror 30 minutes later?

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Question 14

Maria, Peter, Richard and Tina were playing football in the classroom when a window was broken. Maria says, “It was Peter.” Peter says, “It was Richard.” Richard says, “It wasn’t me.” Tina says, “It wasn’t me.” Exactly one child tells the truth. Who broke the window?
  1. Maria
  2. Tina
  3. Peter
  4. Richard
  5. Cannot be determined with certainty

Question 15

Which two tiles complete the puzzle?

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

Question 16

Colour the five rectangles red, blue and yellow so that rectangles sharing a side segment have different colours. How many colourings are possible?

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

Question 17

Goran starts with the stack shown. In one move he reverses the order of some or all blocks taken from the top. What is the smallest number of moves needed to reach the target stack?

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

Question 18

A beaver moves 1 space, a rabbit 2 spaces and a kangaroo 3 spaces per move around the track. They begin at START. The winner lands exactly on FINISH in the fewest complete moves. Who wins?

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  1. The beaver
  2. The rabbit
  3. The kangaroo
  4. The kangaroo and rabbit
  5. The kangaroo and beaver

Question 19

Lonneke wants equal sums in the white and grey cells. Which two numbers should she swap?

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  1. 1 and 11
  2. 2 and 8
  3. 3 and 7
  4. 4 and 13
  5. 7 and 13

Question 20

Gear A turns clockwise. Which two boxes move upwards?

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  1. 1 and 4
  2. 2 and 3
  3. 1 and 3
  4. 2 and 4
  5. Cannot be determined