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… After successfully finishing her first year of studies in Maastricht, Sandra is planning her summer vacation. She wants to visit the eleven largest cities in the Netherlands starting from Maastricht. In the end she wants to return to Maastricht. Can you help her find a route on which she spends as little time as possible in the car? This is what is commonly known as the travelling salesperson problem in Mathematics & Computer Science and one of the most famous problems in Operation Research. It originates in the 19th century and many new algorithmic ideas and techniques have been developed for and tested on instances of this problem. In fact, it is still unknown whether this problem can be solved efficiently for every possible input – a solution would solve one of the seven Millennium Problems which have been selected by the Clay Mathematics Institute in the year 2000. Only one of those has been solved and for the solution of each … you find a route that has an even shorter total distance than one of the two previous ones? 4. One potential way to find the optimal solution to this problem would be the “brute force approach”, i.e. to consider all possible routes and choose the one with the shortest distance. Can you determine how many possible routes there are? If it takes a computer one millisecond to calculate the distance of one route, how long would that approach take? 5. Which companies might face a problem similar to this …