In a bag there are 3 green apples, 5 yellow apples, 7 green pears and 2 yellow pears. Simon randomly is talking fruits out of the bag one by one. How many fruits must he take out in order to be certain that he has at least one apple and one pear of the same colour ?

Two cats, Tom and Bob, caught together 42 mice in three days. Each day, Tom caught twice as many mice as in the previous day, while Bob caught two more mice than in the previous day. Nonetheless, both cats caught the same number of mice for the three days. How many mice did Tom and Bob catch together during the first day ? 

Five children were standing in a line and holding 37 balloons in total. All children who were to the right of Andrew had together 14 balloons; all children standing to the right of Bob had together 32 balloons, the ones to the right of Clara – a total of 20 balloons, and to the right of Danny – 8 balloons. How many balloons did Clara hold ?

Mary wrote a number on each face of a cube ABCD.EFGH. Then, for each vertex, she added the numbers on the three faces sharing that vertex ( for example, for vertex B she added the numbers on faces BCDA, BAEF and BFGC ). The numbers computed by Mary for vertices C, D and E were 14, 16 and 24, respectively. What number did she compute for vertex F ?

A train has 12 coaches. Each coach has the same number of compartments. Mike is travelling in the third coach and in the 18^th compartment from the engine. Jane sat in the 7^th coach in the 50^th compartment from the engine. How many compartments are there in each coach ? 

In how many ways can you place the three kangaroos in three different cells, out of the seven cells below, so that no two kangaroos are neighbours ?

Four points lie on a line. The distances between them are, in increasing order: 2, 3, k, 11, 12, 14. What is the value of k ?

Basil used small cubes with side 1 to construct a cube with side 4. After that, he painted 3 faces of the big cube red and the other 3 faces blue. After her finished, there was no small cube with 3 red faces. How many small cubes have both red and blue faces ?

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

66 cats signed up for the contest MISS CAT 2013. After the first round 21 were eliminated because they failed to catch mice. 27 cats out of those that remained in the contest had stripes and 32 of them had one black ear. All striped cats with one black ear got to the final. What is the minimum number of finalists ?

A 2 x 2 x 2 cube is to be constructed using 4 white and 4 black unit cubes. How many different cubes can be constructed in this way ? ( Two cubes are not different if one can be obtained by rotating the other )

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 ?

Alice forms 4 identical numbered cubes using the net shown. She then glues them together to form a 2 x 2 x 1 block, as shown. Only faces with identical numbers are glued together. Alice then finds the total of all the numbers on the surface of the block. What is the largest total that Alice can get ?

Matthew is catching fish. If he had caught three times as many as he actually did, he would have 12 more. How many fish did he catch ?

 A cake weight 900g. 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 weight 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 addition beside, 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 ?

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

What is the perimeter of the rectangle ?

A Ferris wheel has 32 passenger cabins. If you are sitting in cabin 14 which is  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 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 ?

Which tile must be added to the picture so that the light grey area is as large as the black area ?