Bob is going to visit four cities. He will start from and end up in his home town. The figure shows a map of the regions with the cities. The roads are only along the grid lines. Bob wants to make the trip as short as possible. Which route should Bob follow ?

A rectangle with a perimeter of 34 cm was divided into two smaller rectangles with perimeters 28 cm and 30 cm, as shown in the figure.

What is the area of the big rectangle ?

Which answer completes the addition tree ?

Nathalie wanted to build a large cube out of lots of small cubes. How many cubes are missing from the picture on the right that would be needed to build the large cube on the left ?

How far must Maria walk to reach her friend Bianca ?

Nick can turn right but not left on his bicycle. What is the least number of right tuns he must make in order to get from A to B ?

Anna, Bob and Chris are altogether 31 years old. How old will all three be altogether in three years time ?

In the following multiplication the same digit is used in each square:

Which digit must be used so that the calculation is correct ?

Michael must take a tablet every 15 minutes. He takes the first at 11:05. When does he take the fourth ?

Anne has a few grey tiles like the one in the picture.

What is the maximum number of these tiles that she can place on the 5x4 rectangle without any overlaps ?

The number 36 has the following property: 36 can be divided by its units digit without a remainder ( 36 is divisible by 6 ). With the number 38 this doesn’t work. How many numbers between 20 and 30 have the same property as 36 ?

Maria drew the following figures on square sheets of paper.

How many of these figures have the same perimeter as the square sheet of paper itself ?

Patricia drives one afternoon at a constant speed to her friend. She looks at her watch as she leaves and when she arrives. In which position will the minute hand be when she has completed one third of her journey ?

Johann stacks 1x1 cubes on the squares of a 4x4 grid. The diagram on the right shows how many cubes were piled on top of each other on each square of the grid. What will Johann see if he looks from behind ( hinten ) at the tower ?

36 children voted for five students from their class. Each child was only allowed to vote one. The winter received 12 votes, and the student placed last just 4 votes. If each student received a different number of votes, how many votes did the second placed student receive ?

A 1 x 1 x 1 cube is cut out of each corner of a 3 x 3 x 3 cube. The picture shows the result after the first cube is cut out. How many faces will the final shape have ?

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

In the last game of the hockey match there were lots of goals. In the first half 6 goals were scored and the visiting team were leading. After the home team scored another three goals in the second half, they won the match. How many goals did the home team score in total ?

Which of the figures below will cover the most dots when laid on the square shown on the right ?

Matthias is catching fish. If he had caught three times as may fish as he has actually caught, he would have 12 more fish. How many fish has he caught ?

Numbers are written in the 4 x 4 grid: any two numbers in neighbouring squares should have a difference of 1, that is squares that share an edge. The number 3 is already given. The number 9 will be used somewhere in the grid. How many different numbers will have been used once the grid is filled in completely ?

Two buttons with smiling faces and two buttons with sad faces are in a row as shown in the picture. When you press a button the face changes, and so do the faces of the neighbouring buttons. What is the minimum number of button presses needed so that only smiling faces can be seen ?

40 boys and 28 girls hold hands in a big circle. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl ?

If you start with three number, the “addition machine” produces three new ones by adding together each pair of two. For instance from the numbers {3, 4,6} the addition machine makes {10, 9, 7}. If you use the addition machine again these numbers become { 16, 17, 19}. We feed the three numbers { 20, 1, 3 } into the addition machine and let the machine calculate 2013 times. What is the biggest possible difference between two of the three resulting numbers ?

From an old model train set there are only idential pieces of track to use. Matthew puts 8 such pieces in a circle ( picture on the left ). Marten begins his track with 2 pieces as shown in the picture on the right. He also wants to build a closed track and use the smallest number of pieces possible. How many pieces will his track use ?