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IKMC 2023 - Grades 5-6 - Set 2 - Self-study

Question 1

Holger fills the table with the numbers 1 to 40, following the pattern shown. Which piece could he cut from it?

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Question 2

The digits can be built from matchsticks as shown. Both 15 and 8 use seven matchsticks. What is the largest positive integer that can be built with exactly 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 one straight line?
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Question 4

Rosalinde folds the marked net 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 the same height. 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 disc immediately 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 are wrapped around the parcel. In what order, 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

Which pair of the four puzzle pieces can be combined to make the hexagon shown, without gaps or overlaps?

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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 disc has three holes and is placed over the clock face. It can be rotated about its centre. Which three numbers can appear simultaneously?

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

Question 10

Jonte glues the grey semicircle and two white quarter-circles shown onto the black circle. Which pattern can he not obtain?

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Question 11

Francesca writes three consecutive two-digit numbers in order, replacing digits with symbols: $\square\diamondsuit$, $\heartsuit\triangle$, $\heartsuit\square$. Which number comes next?
  1. $\square\heartsuit$
  2. $\square\square$
  3. $\heartsuit\heartsuit$
  4. $\diamondsuit\square$
  5. $\heartsuit\diamondsuit$

Question 12

The patio is tiled with squares of three sizes. The smallest squares have perimeter 80 cm. What is the length of the snake shown?

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  1. $380\text{ cm}$
  2. $400\text{ cm}$
  3. $420\text{ cm}$
  4. $440\text{ cm}$
  5. $1680\text{ cm}$

Question 13

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

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Question 14

Maria, Peter, Richard and Tina broke a classroom window while playing football. Maria says, “It was Peter.” Peter says, “It was Richard.” Richard says, “It was not me.” Tina says, “It was not me.” Exactly one child tells the truth. Who broke it?
  1. Maria
  2. Tina
  3. Peter
  4. Richard
  5. Cannot be determined

Question 15

Which two numbered tiles complete the puzzle without gaps or overlaps?

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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

Lukas colours the five rectangles red, blue and yellow. Rectangles sharing a side segment must 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 may take any top group of blocks and reverse its order, as illustrated. What is the smallest number of moves taking the initial stack to the target stack?

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

Question 18

On the circular track, the beaver moves 1 space per move, the rabbit 2 and the kangaroo 3. All start at START and must land exactly on FINISH. Who uses the fewest complete moves?

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  1. Beaver
  2. Rabbit
  3. Kangaroo
  4. Kangaroo and rabbit
  5. Kangaroo and beaver

Question 19

Ionneke wants the sum in the white cells to equal the sum in the grey cells. Which pair of 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