IKMC 2027 - Grades 3-4 - Self-study SET 7 - Thematic Batch 3

Four solids are shown below.
Using two of the four solids, which of the following shapes can we NOT make?

Find the number that belongs in the circle marked “?”.

The Maya were an ancient South American people. They used dots and bars to represent numbers. Some examples are shown below.
Using this representation, what is the value of the expression shown?

A library has about 2010 books. A teacher asks Ana, Bea and Carlos to guess the exact number. Ana guesses 2010, Bea 1998 and Carlos 2015. The teacher says their guesses differ from the true count by 12, 7 and 5 books, not necessarily in that order. How many books are there?

Figures X and Y form a “pair”. Which figure below forms a pair with G?

Which of 12, 10, 18, 20 and 15 can be written both as the sum of 3 equal numbers and as the sum of 5 equal numbers?

Sophie draws kangaroos. The first is blue, the second purple, the third red, the fourth black, the fifth yellow, the sixth blue, and the colours keep repeating. What colour is the seventeenth kangaroo?

Starting from the year 2013, what is the smallest number of years we must wait until the product of the year’s digits exceeds their sum?

The figure is a grid of equally spaced black dots. Squares are drawn with their vertices at these dots. How many different square areas are possible?

Anna has a hexagonal glass tile with animal pictures. She flips it successively across the black lines to reach the last position on the right, as shown.
What will the tile look like there?

George’s lesson starts at 5 p.m. He needs 5 minutes to walk from home to the bus stop, exactly 15 minutes on the bus, and another 5 minutes to walk to class. A bus leaves the stop every 10 minutes starting at 6 a.m. What is the latest time George can leave home and arrive on time?

John writes a letter to Peter. One day later, Peter copies it and sends copies to 2 other friends. One day later, each of those friends copies it and sends copies to 2 others. Everyone who receives a letter sends copies to 2 others the following day. By the end of day 5, how many letters have been written?

Sara has 16 blue marbles. She can trade in these two ways:
• 3 blue marbles for 1 red marble.
• 2 red marbles for 5 yellow marbles.
What is the greatest number of yellow marbles she can obtain?

A cube of edge length 3 cm is painted grey before being cut into cubes of edge length 1 cm.
How many small cubes have exactly two painted faces?

Alice is asked to add 27 to a number. By mistake she subtracts 27 instead. How much smaller is her result than the correct result?

A class has 30 pupils. The number of boys is exactly four times the number of girls. How many girls are in the class?

Rabbit has plenty of cheese , Mouse has jars of honey , and Bear has carrots . Rabbit wants carrots, but Bear will trade carrots only for honey. Rabbit must first trade cheese with Mouse for honey, then trade the honey for carrots.
The exchange rates are shown below.
What is the smallest number of pieces of cheese Rabbit must trade to obtain 6 carrots?

Masha, Sasha, Dasha and Pasha sit on a bench as shown.
First Masha swaps places with Dasha. Then Masha swaps places with Pasha. Which two friends are now in the middle?

Try this with a triangle whose three sides are equal, and you will see it.

Source context: for a shape, the number of symmetry axes is the number of ways to fold it into two coincident halves, not the number of successive folds.

Editorial scored task: draw or identify every symmetry axis of an equilateral triangle. Explain how each fold makes the halves coincide, and explain the distinction from repeated folding without unfolding.

Which type of footprint occurs a different number of times in the two pictures?