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… way that the sum of any two adjacent numbers is a perfect square. (a) Given this order, what is the sum of the first and last number? Now, suppose that instead numbers from 1 to 15, we use the numbers from 1 to n. (b) What is the smallest value of n, with n � 15, for which no order exists such that the sum of any two adjacent numbers is a perfect square? Problem 3. Bert has a collection of 7 identical red marbles and a large number of iden- tical blue marbles. He decides to arrange his 7 red … that meets this optimality criterion. Figure 1 Figure 2 Figure 3 Which one has minimal total length? (i) Figure 1 (ii) Figure 2 (iii) Figure 3 (b) Today, I was a bit clumsy, and I dropped a square glass mirror which broke into several sharp pieces when it hit the ground. Then I noticed that all the pieces happened to be triangles with acute angles only (so, all angles were strictly less than 90 degrees). Into how many pieces did the mirror break at least? (i) 6 (ii) 7 (iii) 8 (iv) 9 (c) The Council of Eleven (de Raod vaan èlf) of the Maastricht Carnival Association “De Tempeleers” went on a business trip to New York. They all booked different hotels in a part of Manhattan where the roads form a rectangular grid of Streets and Avenues. Below is a map of their locations. They would like to meet at a convenient location in town, such that the total distance they …

… is drawn in through the working opening, thereby creating an air curtain. The recirculating air passes through a HEPA filter. The air that is exhausted at the top also passes through a HEPA filter. A HEPA filter removes more than 99.97% of particles with a diameter greater than 0.3 micrometers from the air. A BSC is compulsory for work with microorganisms of containment level 2 or higher, where there is a risk of contamination through the inhalation of aerosols. In addition, the cabinet is used for sterile work such as with cell cultures or when working with non-volatile carcinogenic or reprotoxic substances. In order to protect both the researcher and the experiment to the fullest extent possible, the BSC must be used properly and must be properly cleaned and maintained. Maintenance is … disinfectant. • Collect the materials that are required for the work beforehand. • Avoid disruptions to the airflow (downflow): o Do not place materials on the air grids. o Place all requisite materials in the cabinet. o Do not use Bunsen burners, as they can disrupt the downflow. o Keep activities inside the cabinet to a minimum; make as few movements as possible. o Movements should be slow and calm. • After liquid spillages, check the area under the workbench for contamination and clean, if …

… work pressure can sometimes make it difficult to do so. Hopefully, the extension of our workforce in recent years will prove to have been a step in the right direction. In the very near future the broad Work Pressure Task Force will publish its report with recommendations on possible further measures to be taken. While there is no doubt that people need time off to ensure a good work-life balance, we have observed that unused leave entitlements are still growing every year at UM. Perhaps you yourself are among the colleagues who carry over a great many hours of leave at the end of each calendar year. We would like to sincerely encourage all of you to use your leave hours in the year for which they are intended. Should you experience undue restrictions when planning and taking leave, we suggest that you contact your line manager immediately. By taking your accrued hours of leave in a timely fashion, you will also be helping the University to pursue a more effective financial policy. This is because …