Each of the 9 line segments in the figure is to be coloured either blue, green or red. The three sides of each triangle are to have three different colours. Three of the line segments have already been coloured, as shown. What colour can the line segment marked with x have ?

The figure shows an addition where the numbers are coded by letters. Equal letters represent equal digits, and different letters represent different digits. Which digit does the letter X represent ?  

Carla wants to fold a cube from a paper net. My mistake she drew 7 squares on her sheet instead of 6 squares. Which square(s) can she remove so that the figure remains connected and Carla can fold a cube from it ?

In a four – digit number $\overline{ABCD}$  the digits A, B, C, D are in increasing order from left to right. What is the largest possible difference $\overline{BD}-\overline{AC}$ of the two digit numbers $\overline{BD}$  and $\overline{AC}$  ?

Tom used 6 squares with sides of length 1 to form the shape in the piture. What is the perimeter of the shape ?

Kangarina discovered that someone had eaten her jar of honey. She suspected one of her four neighbours: the antelope Anty, the bear Beary, the fox Foxy or the lion Leo. Anty stated that Beary ate the honey. Beary stated that it was Leo. Foxy and Leo denied eating the honey. Who ate the honey if only one of them is telling the truth ?

Square paper sheets of two sizes are needed for an art project. How many of the smaller sheets are needed to cover one of the larger sheets if it is known that the perimeter of one of the larger sheets is eight times as great as the perimeter of one of the smaller sheets ?

On Jump Street, there are 9 houses in a row. At least one person lives in each house. Any two neighbouring houses together are inhabited by at most six people. What is the largest number of people that could be living on Jump Street ?

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 ?