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 ?

2013 people live on an island. Some of these people are truthtellers and the others are liars. The truthtellers always tell the truth whereas the liars always lie. Each day one of the people says “ when I have left the island the number of truthtellers will be the same as the number of liars”. Then he leaves the island. After 2013 days there is no longer anybody living on the island. How many liars were living there to begin with ?

What is the value of 162 + 1620 + 6201 + 2016 ?

Which of the following five expression is correct ?

A large truck can carry 6.3 tons and costs 1000 dollars to rent. A small truck can carry 2.1 tons and costs 400 dollars to rent. To transport 12.6 tons, how much cheaper if only large trucks are rented, compared with only small trucks are rented ?

Mick is in one of the eight squares round a house, and the house is to his north-west. On which square is Mick ?

The table below summarizies the results of a test in a certain class. What is total score of this class ?

In reading a story book, Lance reads one page more each day than the preceding day. On the fourth day, he reads 39 pages. After 9 days, he still has 48 pages to go. How many pages are there in this book ?

The contents of the five boxes are labeled. A ball is drawn at random from each box. From which box is the drawn ball most likely to be red?

Gasoline costs 6 dollars per liter. A car uses up 8 liters for every 100 km. What is the largest integral number of km that can be covered with 200 dollars worth of gasoline ?

The chart below shows the sale figures of a certain merchandise in 2014 and 2015 by the season. How many more items were sold in 2015 than in 2014 ?

Fanny has 20 coins each worth 5 pence. Trading some of them for coins each worth 2 pence, she ends up with 32 coins. Then she trades some more 5-pence coins for coins each worth 1 penny, and now she has 56 coins. How many 5-pence coin does Fanny still have ?

Every pair of the numbers from 1 to n is added, and there are 215 different sums. What is the value of n ?

In a library, 12.1% of the books are fictions. After 1800 fictions and 2400 non-fictions go on loan, only 12% of the remaining books are fictions. How many books are there in the library initially ?