A pin is connected perpendicular to the centre of a circular disk as shown. A little push will make it roll over a grey circle. How many turns does it take to come back to its original position? (The pin makes 30° with the ground and the distance from the pin tip to the contact point is 10 cm.) [Figure: see page 5 of source PDF]

How many fonts have been used to write the letter Q in the image shown below? [Figure: see page 5 of source PDF]

How many surfaces are there in the letters of the word sign 'DESIGN'? Two views of the sign are shown below. [Figure: see page 4 of source PDF]

Robert loves fruits. With his monthly allowance, he can buy either 50 apples or 40 bananas. One month, he decides to save 10% of his allowance. After buying 20 bananas, how many apples can he buy?

A cube is dissected by one plane at 1/6 side length and one plane at 1/2 side length in each of the three dimensions of xy, yz and xz. How many cubes will be formed after dissecting the large cube?

Count the number of triangles in the image below. [Figure: see page 3 of source PDF]

Shown below is a number puzzle (4×4 sliding puzzle; rows: 10 8 3 14 / 7 5 12 2 / 4 9 x 11 / 13 1 15 6). Only one piece can be slided horizontally or vertically in one move. What is the least number of moves required to bring the piece with number 10 to the empty position x? [Figu…

Imagine a pentagon shaped building. The walls of the building are sides of the pentagon, and there is a watchtower at each vertex. Each watchtower can have guards who can watch two walls connected to the watchtower. What is the minimum number of guards required if each wall needs…

The two objects on the left have a height of 1 cm and sides of 4 cm. The yellow object on the right has a total height of 5 cm. The cylindrical base of the yellow object has a diameter of 6 cm and a height of 1 cm. The two objects on the left are to be stacked on the yellow objec…