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 hae three different colours. Three of the line segments have already been coloured, as shown. What colour can the line segment maked 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. By 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 ?

The number 100 is multiplied either by 2 or by 3, then the result is increased either by 1 or by 2, and then the new result is divided either by 3 or by 4. If the final result is a natural number, what is this final result ?

In a four-digit number $\overline{ABCD}$ , the digits A, B, C and 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 $\overline{AC}$ ?

Kangarina discovered that someone had eaten her jar of honey. She suspected one of her four neighbour: the antelope Anty, the bear Beary, the fox Foxy or the lion Leo. Anty statted 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 ?

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

Square paper sheets of 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 taking 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 has 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. 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 belows, so that not 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 ?