IKMC 2027 - Grades 5-6 - Self-study SET 4 - Thematic Batch 3

Bin and Bob play a can-knocking game. They throw balls at two initially identical towers, with the same point values in the same positions. Bin knocks down 6 cans and scores 25 points. The picture shows the remaining towers. Bob knocks down only 4 cans. What is his score?

Five positive integers a, b, c, d, e have sum 2017 and are placed in a row so that adjacent numbers differ by 1. What is c?

Susi, Lisa, Andi and Eve spend Sunday morning in the park. They start together at the flag and choose four different routes to the playground. The source says that Susi arrived, then Eve, and Andi arrived last. All four travel at the same speed. How far did Lisa travel?



Editorial clarification: The intended order is Susi first, Eve second, Andi last. The source omits the word “first”.

Eva and Olga are girls; Adam, Isaac and Urban are boys. A girl holding the ball may throw it to any other player. A boy must throw it to another boy, but not the player who just passed it to him. Eva initially holds the ball and throws it to Adam. Who makes the fifth throw?

The digital clock shown reads 20:19. What is the next time it will display the same four digits? Select the corresponding picture.

Mickey has four friends: Donald, Minie, Goofy and Daisy. Minie visits daily, Donald every 2 days, Goofy every 3 days and Daisy every 4 days. Yesterday all four visited together. At least how many more days from today until they next visit together?

A rectangular school playground has perimeter 32 m, and its length exceeds its width by 4 m. The main building runs along one long side. Trees are planted around the playground at 1 m intervals, with a tree at each of the two corners opposite the school. How many trees are planted?



Editorial clarification: No trees are planted on the building side, including its two endpoints.

Tom has six straight sticks of lengths 1, 2, 3, 2018, 2019, 2020 cm. In how many ways can he choose three to form a triangle?

A city has 6 horizontal and 6 vertical roads forming 36 intersections. Flowers grow at every intersection. A watering truck must visit them all on a closed route, starting away from an intersection. What is the least number of turns it must make?



Editorial clarification: Follow the shown horizontal and vertical roads; count a change between them as a turn.

Alice has the decorated piece of card shown. Which house cannot be folded from it?

A class has 50 pupils. Thirty like Pepsi, 21 like Coca, and 7 like both drinks. How many like neither drink?



Editorial clarification: Find the number who like neither drink.

Two snails start together at A and crawl around the rectangular grid garden in opposite directions. The faster snail travels twice as fast as the slower. Where do they meet for the first time after leaving A?



Source correction: The original diagram labels the upward snail slow and the rightward snail fast. These directions give Q (B); the printed source key T (D) is wrong. Figure labels: chậm = slow; nhanh = fast.

Ben has five equal rectangular cards, each bearing one natural number on each side. They are placed without rotation or reflection into positions I–V on the board shown, so that touching sides have equal values. Which card can occupy I?

Square ABCD has side 4 cm. E is the midpoint of AD and F is the square’s centre, as shown. What is the area of triangle BEF?

Mrs Brown has more than 2 and fewer than 8 grandchildren. She gives all of them equal numbers of whole cakes. Which number cannot be the total she distributes?

Tom draws three parallel lines and two perpendicular lines intersecting them. Some angles are marked in the picture. What is the angle marked with a question mark?

Thirty-six water-lily leaves are arranged as shown. A frog starts on a corner leaf. It may jump horizontally or vertically, skipping at least one leaf each time, and never lands on a leaf twice. Including its starting leaf, what is the maximum number of leaves it can visit?

On Evenland, people use only even digits. Their positive integers in increasing order begin 2, 4, 6, 8, 20, 22, 24, ... What is the 100th number?

A rectangle is divided into squares as shown. If the smallest black square has area 1 cm², what is the perimeter of the rectangle in centimetres?

A dartboard has scoring rings as shown. Tom throws 9 darts and never misses. Counting only how many darts hit each ring, in how many ways can he score 27?