Sixty six cats signed up for the contest MISS CAT 2013. After the first round 21 cats were eliminated because they failed to catch a mouse. Of the remaining cats, 27 had stripes and 32 had one black ear. All striped cats with one black ear got to the final. What is the minimum number of finalist ?

There are four buttons in a row as shown below. Two of them show happy faces, and two of them show sad faces. If we press on a face, its expression turns to the opposite ( e.g.a happy face turns into a sad face after the touch ). In addition to this, the adjacent buttons also change their expressions. What is the least number of times you need to press a button in order to get all happy faces ?

40 boys and 28 girls stand in a circle, hand in hand, all facing inwards. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl ?

A stack of loads must be transported. If Ann does the job alone, it will take one hour. If Ben does the job alone, it will take two hours. How long will it take if Ann and Ben do the job together ?

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 ?