How many 3 –digit numbers possess the following property: after subtracting 297 from such a number, we get a 3-digit number consisting of the same digits in the reverse order ?

When Pinocchio lies, his nose gets 8 cm longer. When he says the truth, the nose gets 3 cm shorter. When his nose was 7 cm long, he said five sentences and after that his nose got 25 cm long. How many of Pinocchio’s sentences were true ?

There were 2013 inhabitants on an island. Some of them were knights and the others were liars. The knights always tell the truth and the liars always lie. Every day, one of the inhabitants said: “ After my departure the number of knights on the island will equal the number of liars” and then left the island. After 2013 days, there is nobody on the island. How many liars were there initially ?

Starting with a list of three number, the “ changesum” procedure creates a new list by replacing each number by the sum of the other two. For example, from { 3; 4; 6} the procedure “ changesum” gives { 10, 9, 7 } and a new “changesum” leads to { 16, 17, 19 }. If we begin with the list { 20, 1, 3 }, what is the maximum difference between two numbers of the list after 2013 consecutive “changesums” ?

Alice forms four identical numbered cubes using the net shown.

She then finds the total of all the numbers on the surface of the block.

What is the largest total that Alice can get ?

A cake weighs 900 g. Paul cuts it into 4 pieces. The weight of the largest piece is the same as the total weight of the other three pieces. What is the weihgt of the largest piece ?

Two big rings – one grey, one white – are linked to each other. Peter, in front of the rings, sees the rings as in the picture:

Paul is behind the rings. What does he see ?

In the following addition, some of the digits have been replaced by stars.

What is the sum of the missing digits ?

What is the difference between the smallest 5-digit number and the largest 4-digit number ?

A square of perimeter 48 cm is cut into 2 pieces to make a rectangle ( see the picture )

What is the perimeter of the rectangle ?

Katrin has 38 matches. She built a triangle and a square, using all the matches. Each side of the triangle consists of 6 matches. How many matches are in each side of the square ?

A Ferris wheel has 32 passenger cabins. If you are sittin in cabin 14 which ic currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel ?

The pearl necklace in the picture contains black pearls and white pearls.

Arno wants to have five of the black pearls. He can only take pearls from either end of the necklace, and so he has to take some of the white pearls also. What is the smallest number of white pearls Arno has to take ?

Harry participated in a broom flight contest which consisted of five laps. The times when Harry passed the starting point are shown in the table. Which lap took the shortest time ?

It takes Ben 30 minutes to cut a long log of wood into six pieces. How long does it take him to cut another log of wood into nine pieces ?