How many different squares of any size can you identify in the picture ?

Max, David and Peter completed in an ice cream eating contest. Max ate 6 scoops in the same time as David ate 4 scoops and Peter ate 5 scoops. Max ate 18 scoops in half an hour. How many scoops in total did they eat in half an hour together ?

From a wooden cube with side 3 cm we cut out at the corner a little cube with side 1 cm ( see picture ). What is the number of faces of the solid after cutting out such a small cube at each corner of the big cube ?

How many pairs of two-digit natural numbers have a difference equal to 50 ?

During the final game of a soccer championship the teams scored a lot of goals. Six goals were scored during the first period of the game and the guest team was leading the score at the halftime break. During the second period, the home team scored 3 goals and as a result, they won the game. How many goals did the home team score altogether ?

In the squares of the 4 x 4 board numbers are written such that the numbers in adjacent squares differ by 1. Numbers 3 and 9 appear in the table. Number 3 is in the top left corner as shown. How many different numbers appear in the table ?

Aron, Bern and Carl always lie. Each of them owns one stone, either a red stone or a green dtone.

Aron says: “ My stone is the same color as Bern’s stone”.

Bern says: “ My stone is the same color as Carl’s stone” .

Carl says: “ Exactly two of us own red stones” .

Which of the following statements is true ?

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” ?