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

A kangaroo appears in the first triangle on the left. The dashed lines act as mirrors, reflecting it successively into the neighbouring triangles. What will the kangaroo look like in the last, shaded triangle?

John has a card made of decorated squares, as shown. Which cube can he fold from this net?

A and B are opposite vertices of the rectangular box shown. How many shortest paths along its edges lead from A to B?

At her birthday, Emily takes photographs with her eight friends. Each friend appears with her in either two or three photographs, and each photograph shows Emily with exactly five friends. How many photographs does she take?

Four cards lie in the order shown. Which listed order cannot be obtained by swapping just two cards once?

John uses 15 matches to form five small square cells as shown. What is the least number he must remove so that exactly three squares remain and every remaining match belongs to a square boundary?



Source clarification: The five stated squares are the small cells; the figure also contains a larger square, which must be counted in the final total.

Three dice are stacked as shown. Opposite faces sum to 7, and the two faces touching at each join sum to 5. How many dots are on face X?

David has three sisters and five brothers. His sister Alice has s sisters and b brothers. What is s×b?

On planet DOT, everyone has twice as many dots on their hands as their age in years. Simi is 10. Her mother has 66 dots and is three years younger than her father. How many dots do Simi and her parents have altogether?

Peter defines a special way of adding shapes. The two examples illustrate his rule. Find the rule and complete the last addition.





Editorial convention: Superimpose shapes and erase their common segments.

Jenny has a solid cube made from 125 unit cubes. She removes some cubes to make the holes shown. How many unit cubes remain?



Editorial interpretation: The three pictured 1×3 openings are straight tunnels all the way through the cube, with constant cross-sections.

In three practice football matches, the Little Stars score three goals and concede only one. They win once, lose once and draw once. What is the score of their win?

William Turner boards the Black Pearl to rescue Elizabeth. There are at least two pirates. The first says, “There are 12 of us,” then jumps overboard. Each subsequent pirate says, “Everyone who jumped before me is a liar,” before jumping. This continues until no pirates remain. How many pirates tell the truth?

Yesterday Sam went to a film with her mother. It ran from 13:47 to 16:18. How many minutes did it last?

Squares I and II in the diagram have perimeters 16 m and 24 m respectively. What is the perimeter of square IV?

Place the numbers 1 through 14 around the circle, one in each small circle, so that neighbours differ by 1 or 2. Which listed pair is adjacent?

The number 2018 has four different digits and its last digit is four times its first. How many four-digit numbers have these properties?

How many ways can a five-petalled flower be coloured red and yellow, one colour per petal, if rotations of the same colouring count as one?

Cards numbered 1 through 8 are placed in boxes A and B with equal total values. Box A contains exactly three cards. Which statement is correct?

Tarzan counts 54 animals. Of them, 37 can fly, 25 walk and 20 swim; 13 can both fly and walk, 12 fly and swim, and 11 walk and swim; 5 can do all three. How many can do none of these activities?



Editorial clarification: Count animals with none of the three abilities.