There are eight balls numbered with the numbers 40, 80, 100, 101, 190, 200, 260 and 292 in a bag. Martina takes four balls out of the bag and calculates the sum of the numbers on these balls. It appears that this sum is half of the sum of the numbers on the balls that remain in the bag. What is the greatest number written on the balls taken out ?

The structure on the figure is made of unit cubes glued together. Morten wants to put it into a rectangular box. What are the dimensions ( length, width and height ) of the smallest box he can use ?

Four players scored goals in a handball game. All of them scored a different number of goals. One of the players, Mike, scored the least number of goals. The other three players scored 20 goals in total. What is the largest number of goals Mike could have scored ?

Ala likes even numbers, Beata likes numbers divisible by 3, Celina likes numbers divisible by 5. Each of these three girls went separately to a basket containing 8 balls with numbers written on them, and took all the balls with numbers she liked. It turned out that Ala collected balls with numbers 32 and 52, Beata – 24, 33 and 45, Celina – 20, 25 and 35. In what order did the girls approach the basket  ?

The picture of a kangaroo in the first ( leftmost ) triangle was reflected across the dotted lines, as in mirrors. The first two reflections are shown.

What does the reflection look  like in the shaded triangle ?

The numbers 1, 2, 3, 4 and 5 must be written in the five cells in the figure, resprcting the following rules:

- If a number is just below another number, it must be greater

- If a number is just to the right of another number, it must be greater

In how many ways can this be done ?

John wrote a natural number in each of the four boxes in the bottom row of the diagram. Then he wrote in each of the other boxes the sum of the two numbers in the boxes immediately underneath. What is the largest number of odd numbers that could appear in the completed diagram ?

Julia has four pencils of different colours and wants to use some or all of them to paint the map of an island divided into four countries, as in the picture. Any two countries with a common border must be coloured differently on the map. How many different colourings of this map are possible ? ( Two colourings are considered different if at least one of the countries is coloured differently )

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