Icing on the Cake 2021 by Ideaal! (Abacus)

S Association magazine of W.S.G. Abacus

Interview

54th Board A Day With...

Ruben Hoeksma Tracy Craig

Mathematics problem solving

Icing on the Cake 2021

INDEX 4 4 6 12

Columns External Thoughts The Pen Staff Says Your Story Mathematical A bridge into the first year 16 Statistical analysis of life 21 expectancies

5 5, 24-27 7 8 13, 16, 17 18 22, 23 24

Fun On the couch Dies Cake Review Meme Page A day with... Puzzles Interview 54th Board Reviews Puzzle Solutions

Editorial Dear reader,

so that the ice cream is upside down in their hands, forcing you to grab it in a way where you can twist it to be rightside up. This makes things awkward for both parties, but it must be done. If you order 8 blizzards, then all 8 will be served this way. There are no exceptions. Which is why they offer you a free blizzard when they forget to serve you in this specific way. There is a reason for this of course, Dairy Queen isn’t stupid. The reason they serve you upside down is to prove that the ice cream they give to you is quality. If the ice cream was mixed too much, then the flavor swirls will not be there and the mixins will be tiny pieces and the whole mixture will just fall out of the cup. If the blizzard was not made fresh, and was standing out on the counter for a while, then the sides will melt and then eventually will splatter on the ground if given to a customer. To sum things up, Dairy Queen has an ingenious system of offering people free ice cream when their blizzard is not served upside down. It is a positive way to hide the fact that the ice cream they just served might not be up to the standard that they advertised. So what is your Dairy Queen strategy? Enjoy the fun of it being served upside down, or hope they forget and get another one for free?

since this is the winter edition of Ideaal!, I am going to tell you all about the wonder of getting an ice cream at Dairy Queen. To set the stage, Dairy Queen is an ice cream establishment within the States which is open year round. And while this does not sound exciting at first, there is one important thing that I still need to mention. Dairy Queen has a policy in which your order must be served upside down, otherwise, they provide a coupon where the next ice cream you order will be free. To those who are not lactose pros, this concept might sound abstract. But luckily for you, this is a topic that I am passionate about. Unfortunately, this deal only works for blizzards, which are cups filled with thick ice cream that has toppings and syrups mixed into it. They come in many sizes and different flavors. Each month has their own blizzard to match the vibes of the year. For example, December has Candy Cane Chill and October has Reese's Extreme, and what is more extreme than the month October? That's right, nothing. Now, we can move onto the laws of blizzards. Whether you are in the drive through, at the window, or walk inside to the counter, the rules remain the same. The person serving you must hand you your blizzard upside down. For visualization, they themselves are standing Fia. upright, but they twist their arm Colophon Editorial address: W.S.G. Abacus Postbus 217, 7500 AE Enschede Phone: 053 - 489 3435 ideaal@abacus.utwente.nl www.abacus.utwente.nl Editors: Jorg Gortemaker Tim Hut Daan van Kats Lavinia Lanting Fia Nase Timon Veurink

Guest writers: Margriet Eijken (External Thoughts), Tracy Craig (Staff Says), Martijn Heutink (Puzzle: Chess Tactics), Eva van Laar (A Bridge into the first year), Jorn de Jong (Puzzle: Zig-Zag, Puzzle Solution: Rectangles in a square), David van der Linden (Puzzle: Hexcells Infinite), Renske Idzenga (Statistical analysis of life expectancies), Luuk van der Werf (Review: D.S.V. De Skeuvel), Martijn ter Steege (Puzzle Solution: What's the PIN?).

AGENDA • 12 January 12:45 Homemade Wednesday • 12 January 20:00 Freshmen Pubquiz • 26 January 16:00 End of the semester drink • 2 February 12:45 Homemade Wednesday • 2 February 16:00 Pre-Taipan tournament drink • 2 February 20:00 Taipan tournament

Ideaal! is the magazine issue of Wiskundig Studiegenootschap Abacus and the department of Applied Mathematics. The responsibility for the articles published in this magazine lies with the original author(s). The period of notice of Abacus is four weeks before the end of the association year (August 1st). That means that you must cancel your membership before July 4th. If you have forgotten to cancel your membership before that time, you will pay contribution for another college year. Would you like to cancel your membership? Send an email to board@abacus.utwente.nl.

External Thoughts Text: Margriet Eijken As you might know the theme of this Ideaal! is “Icing on the Cake”. Now you are probably wondering whether this piece will be the Icing on the Cake, well I am sorry to burst your bubble but it won’t be. Writing is not one of my hobbies so I can safely say that this is not going to be a masterpiece. Talking about pieces, I do like a piece of cake every now and then and preferably with icing. Sadly, I usually don’t have a lot of free time for baking but when I do bake I make the most heavy, fattening cakes often with a lot of choco-

late, you can ask my housemates about this. This one time I made an intense chocolate cake that required the staggering amount of 7 bars of chocolate. This translates to 700 grams of chocolate. It was great. Just thinking about it makes me hungry again. But when you want to eat a lot of cake you should also exercise if you want to stay sort of healthy. Now, I am not great at sport in general. Some of you might know that I play table tennis at Thibats here at the sports centre on campus and this is probably one of the very rare sports at which I am not terrible. Unfortunately, when corona started nobody could play sports including me so I picked up running. With this

I discovered that I can add another sport to the list of sports I am not good at. But I did persevere and continued running every once in a while until last September, so I am pretty happy with myself for doing that. I think this perseverance will also come in handy with my function as External Affairs, so the running probably wasn’t for nothing. Now, what is the lesson you can take away from this story? Nothing really, except you learned a little bit more about me :). BTW, if you want the recipe for the cake it’s called “De ultieme verjaardagstaart” from the Allerhande.

The Pen Text: Tim Hut I started in year two of secondary school developing a magic system. For years I would spend hours writing in a spreadsheet keeping track of characters, ideas for stories, magical objects and much more. Since I never know how to write down these stories, the spreadsheet contained mostly just keywords and the rest stayed mostly in my head. Until it became too much. In year six I deleted the spreadsheet and stopped. However because of almost having no physical courses, which meant not having a lot of social contact, I started again last year trying to recreate it from the ground up keeping only the general idea of what I had created before. My magic system is an elemental magic system. Lore wise it contains an infinite amount of elements, but in reality I created only 28 different elements of which the first 15 are only important. The elements are

divided in groups of which the nth group contains n elements. These groups I call the celestial pillars of magic. Written in set notation, the first five groups and their names are: P1 = {unity} # the sphere of unity P2 = {day, night} # the rings of balance P3 = {matter, space, time} # pillar of chaotic magic P4 = {air, earth, fire, water} # pillar of nature magic P5 = {to hear, to see, to smell, to taste, to touch} # pillar of wild magic The story is set mainly in the fictitious city of Ongrad. Here, some teens during the first full moon after their 16th birthday are invited to ceremony to unlock their magic. To do this they touch a tree made out of the fictitious metal magicium from which they also obtain a piece of jewellery through which they can cast their magic. Each person is affiliated with one of the pillars, they can cast spells with all the

elements and have a skill that is specific to that pillar. Someone who is affiliated with chaotic magic can change how mass, distance or time is perceived; someone who is affiliated with nature magic can change and control their environment and someone affiliated with wild magic can change into different animals and enhance their senses. There are only two people who are affiliated with balance, since balance is seen as the source of all magic they have all skills previously mentioned. A someone can’t be affiliated with unity naturally, but with the help from a ‘hidden one’ (the personification of an magical object or location) they can be temporally. Then their magic works similar as with balance. So this is, without going into much detail, what I have been working so now and then. I hope one day I have the confidence to write down some actual plot.

On the Couch... Text: Daan van Kats and Timon Veurink 1. Introduce yourself! W: I'm Wybren, I’m a second years, I like to play volleyball and Taipan. C: I'm Chris and I am from Zwolle, I guess, well, I technically still live here. J: I am Jeroen, I’m also a second year student. I am from Flevoland and I feel like Flevoland is underrepresented right here. P: Hi, I'm Partick and I come from a little village in Twente and I play Taipan for fun. O: Hi, I'm Oisìn, I study mathematics here in Twente, I play rugby and my fun fact is that I have over 70 pairs of socks. P: A true sock collector. J: What are you even doing with those. 2. How long have you been sitting on this couch? All: about 45 minutes. P: Enough for a small game of Taipan. 3. What is your favorite memory on this couch? C: It is actual the first time I sit here. W: Playing Taipan. 4. Who do you prefer to sit on the couch with? P: With the clickerheroes…. and Chris!

5. What is your favorite article in the Ideaal!? P: This on the couch interview. J: All the coupons that will be showing up from now on! (This is not happening, but we love the enthousiasm) 6. Are you a cat or dog person? C: Dog. P: Dog. O: Can’t choose, but I kinda like both. W: Depends on the weather, bad weather, cat, nice weather, dog. J: I’m picking cats, they just do whatever they feel like. 7. What was the highlight of your day? J: The ODE lecture this morning! Or when I woke up this morning and it was too early, so I could sleep a little longer. O: I liked my cup of tea. C: That I went back to bed this morning and skipped the lecture. P: The pretty girl I saw in the bus this morning. J: That I found my water bottle back! 8. What will be the highlight of your day? J: I’m going to Alpha’s. P: I’ll join the Discord server with the boys.

9. If you were in a committee together, how would that committee have been called? J: The Abaclickers! Everyone agrees C: And what would we take care off? We “verklicken” everyone. 10. What is your favorite math theorem? J: The Weierstrass M test. Or the Bolzano Weierstrass Theorem. O: Gauss’s law or the least squares method. C: e^(i*pi) = -1. W: Mine is Pythagoras. 11. What would your perfect lunch be? O: Sushi. C: A softly boiled egg. W: A tosti. Nothing beats a good tosti. P: Pancakes, always pancakes. 12. Cayley or Hamilton? J: I don’t know, But I’m saying Hamilton, purely for the musical. P: I don’t know Cayley, but I hate Hamilton, so I pick Cayley. C: Who?? W: Cayley, who is Cayley? 13. What are you going to do next? W: Cycling to Abacus. C: To a lecture of Hil.

Dies Cake Review: Tarte au Citron by Sem Geerts

dic i c a too ry tasty Structu 7.5 out of t i b crust +re is great, 10. Just ae, but verest nice cr s m A m e o l r i h o t o t t t isp f le too m h lemo for uch lem n yelly y to my l The acidicy of it maiking.on flavour kes it very tasty. I'm a fan! 5

Staff Says Text: Tracy Craig Mathematical problem solving Can you define what “problem solving” is? Or indeed, what is a “problem” at all? One definition of a problem is that it is something that needs to be solved where you don’t know exactly what to do when you begin. If you know what to do, even if it is difficult, then it is an exercise and not a problem. Because by definition problem solving involves not quite knowing what to do, it is hard to teach problem solving and heard to learn to be an effective problem solver. When learning how to solve exercises we can learn certain algorithms, certain theorems, certain techniques. To be an effective problem solver it is advisable to learn certain heuristic strategies, so-called “rules of thumb”. These heuristics include (but clearly are not limited to) draw a diagram, consider special cases, solve a related but simpler problem, work backwards, guess and check, and so forth. An example of “solve a simpler problem” is to first only consider n in N when proving that for all n in R. An example that benefits from “draw a diagram” is to determine for what values of k the equation e2x=kx has only one solution. Many mathematics education researchers have studied problem solving. An early and highly influential resource was George Pólya’s How to Solve It, where he breaks the problem solving process into four steps: • Understand the problem • Devise a plan

• Carry out the plan • Look back The two of those steps most often neglected are the first and last. We often feel that we do understand a problem when, in fact, we do not, or at least not altogether. Taking the time to understand a problem is not time wasted, it is often time saved. Once we have solved (or think we have solved) a problem we are often in a rush to move on to something else. However the act of “looking back” is extremely valuable. Looking back can reveal to us any errors we have made or give us an opportunity to see, in hindsight, other ways we might have tackled the problem. At the very least it can help us internalise what we have done so that we can repeat it in the context of another problem some other day or in a different context. If you want to read educational research into mathematical problem solving I recommend to you the work of Pólya, also Alan Schoenfeld who carried out very interesting and illuminating research into how novices and experts approach problem solving and devised a way of charting problem solving process through “talk aloud” problems. Pugalee has done some wonderful work on metacognition (being aware of how we are thinking) which is a key part of effective problem solving. In my PhD I looked into how the act of writing about one’s problem solving process can help with that crucial first step of “understand the problem” since writing forces you to confront your own understanding (or lack of it). The references provided here are all a bit old, because I have not kept up with the literature on problem solving, but they are all good. If you are interested in reading generally about maths education research you can look at the more theoretical and abstract journals such as Edu-

cational Studies in Mathematics, or Journal for Research in Mathematics Education, or the quite practical journals such as International Journal of Mathematical Education in Science and Technology, and Teaching Mathematics and its Applications. Studying mathematics is great fun, but so is studying mathematics education. Perhaps some of you will choose such an academic future and the world of education will benefit from your contributions. References

Pólya, G. (1945). How to solve it (2nd ed.). Princeton, NJ: Princeton University Press Pugalee, D.K. (2004). A comparison of verbal and written descriptions of students’ problem solving processes. Educational Studies in Mathematics, 55, 27–47. Pugalee, D. K. (2001). Writing, mathematics, and metacognition: Looking for connections through students' work in mathematical problem solving. School science and mathematics, 101(5), 236-245. Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (Reprint). Journal of Education, 196(2), 1-38. Schoenfeld, A.H. (1985). Mathematical problem solving. Orlando, FL: Academic Press G.M.A. Stanic and J. Kilpatrick, Historical perspectives on problem solving in the mathematics curriculum, in The Teaching and Assessing of Mathematical Problem Solving, R.I. Charles and E.A. Silver, eds., Lawrence Erlbaum Associates, Hillsdale, NJ, 1989, pp. 1–22. And finally Craig, T.S. (2016). The role of expository writing in mathematical problem solving. African Journal of Research in Mathematics, Science and Technology Education, 20(1), 57-66. Craig, T.S. (2011) Categorisation and analysis of explanatory writing in mathematics, International Journal of Mathematical Education in Science and Technology, 42(7), 867-878.

Meme page

A Day With... Ruben Hoeksma

This time we had the pleasure of conversing with the General Adjunct of Abacus: Ruben Hoeksma. Ruben started studying Applied Mathematics in Enschede and is back in Twente: at the UT and with Abacus. Text: Lavinia Lanting and Daan van Kats

Ruben Hoeksma, the current General Adjunct and as such board member of the 54th board of W.S.G. Abacus, has been an associate professor at the University of Twente since December 1st of 2019. While this may seem like a short while, Ruben has known the University of Twente for much longer as he himself studied Applied Mathematics here. ‘I started my studies in 2003 and finished my Masters in 2010. I also started my PhD here at the University of Twente that same year and finished it in early 2015, after which I spent half a year as a lecturer here at the university, then 2 years as a postdoctoral researcher in Santiago, Chile, at the University of Chile. After that I spent a bit more than 2 years as a postdoctoral researcher at the University of Bremen, after which I came back here to the University of Twente.’ Ruben has remained connected to both Abacus and the University of Twente even in his absence.

‘I have been a member of Abacus since the very start of my Bachelor studies and there has been all in all just one year during which I stopped being a member. While I was living in Bremen, it occurred to me that so much time had past and that perhaps the moment had come to stop being a member and so I did. Within the year I returned to Enschede and became a member again and I am now even General Adjunct.’

Which courses do you teach throughout the year? ‘In the current quartile I am not doing any teaching unfortunately, but last quartile I was one of the supervisors for the project of Module 1. Next quartile will also be my busiest as I then teach Mathematical Optimisation, which is one of the electives in Module 11, and I am also the coordinator of the project in Module 7. I also do some teaching in Module 4 as I then give the course Introduction to Python.’

These are all of the courses that Ruben teaches to Applied Mathematics students, but they are certainly not all the courses he currently teaches or will teach in the future. ‘I am currently still finishing my UTQ (University Teaching Qualification, which means I now have a bit less teaching than I would otherwise. I will finish it this year, after which I will be able to do some more teaching, which will probably be in the Mathematics Line. I have already taught a few of these courses throughout the past year, but my teaching is currently mostly filled with courses for Applied Mathematics students, which is generally nicer than so-called service teaching as Mathematics students are usually more interested in mathematics, although I would argue that these courses can be very satisfying as well. Students from other studies generally struggle more with mathematical topics and it’s fun to figure out in which different ways you can approach and teach a

certain topic.’

How does your day tipically start? ‘Well, my typical working day sort of starts the moment I get out of bed and check my e-mails on my phone. It’s not the best thing to do, but like for many other people the phone is an extension of myself. In addition, I get my work e-mail everywhere: on my phone, on my tablet, on my laptop. I can never get away.’ After getting up, Ruben gets behind his desk, either at home or at the university, and starts up his computer to check his e-mail once again, as the e-mails partly dictate what he has to do on a given day as a sort of to-do list including all tasks that still have to be completed. ‘Like everybody these days, even the students, I have a lot of meetings. Usually my day is comprised of teaching, although not currently, reading through my e-mails, meetings and getting organisational tasks done based on those last two. I also always try to reserve some time for research. The latter usually entails me reading new and old material regarding the subject or working on some problem, possibly in collaboration with others.’

Is this very different from your typical working day before Covid? ‘I haven’t had that many working days before Covid-19, unfortunately, and in the first 2 months that I was working at the University of Twente I was still going back and forth between Enschede en Bremen. I was about 3 days per week in Enschede and 2 in Bremen and my days in Enschede were mostly

consisting of the educational tasks I had at the time.’ Ruben admits that he believes that his working experience has not being representative of what it would look like under normal circumstances. ‘I would envision a normal day to have more time to interact with colleagues and students.’ He in addition adds:‘There is no typical working day for me though since I have some fixed tasks on certain days. On Mondays I start my day by joining the board meeting after doing some other small tasks. I also try to have some other meetings planned shortly after. On most Fridays I have a Faculty Council meeting. Those are also in the morning from 10:45 to somewhere during lunch. Hence Friday mornings I dedicate to tasks for the Faculty Council and I then try to keep the rest of my day empty for research. Most educational tasks take place between Tuesdays and Thursdays.’

Is there a difference between here and the other countries you worked? ‘The tasks may be not too different, but my position definitely changed. As an assistant professor I have a lot more organisational tasks compared to when I was a postdoctoral researcher. I had almost no responsibilities and used to work almost exclusively on research. When I was in Chile, I had no educational tasks. In Bremen I also had no educational obligations, but I chose to dedicate some of my time to education. Currently about half of my time is spent on educational tasks.’

What is your favourite part of

your work and why? ‘I like all aspects of what I do. What I do notice very often about myself is that, sometimes, after completing a certain task, I feel that I spent too much time on that task. On the other hand, I am a perfectionist, so this happens quite often and while carrying out my task I enjoy perfecting what I am doing. As for what I really enjoy the most, I am not a huge fan of organisational tasks that I have to do or end up doing. These sort of tasks I like much less than preparing a lecture or having contact with the students and discussing about mathematics, but they are necessary. The university doesn’t run itself. By this I don’t mean to say that teachers run the university, but we definitely play a role.’

When and how did you become interested in mathematics? ‘I think about it sometimes and I’ve had this question before as well. What I always say is that there wasn’t a single moment. I feel like it’s more of my nature and my nurture as well. As far as I know, I’ve always liked logic and numbers. Even in primary school I liked all the computational classes and excelling at something definitely helps a passion to grow. I’ve also always had this interest in computer programming. I started when I was about 11 or 12, which was quite early for the time.’ Ruben first came into contact with mathematics in high school. He felt it was so easy he naturally started spending less and less time on it even though it was clear to him that mathematics could be a very interesting topic, although this may sound quite contradictory. ‘Usually, the tasks I had to do in

school were not that interesting or necessary for me and my teachers also felt that was the case. So even though I spent a lot of time on mathematics, it wasn’t on the mathematics taught in school or even on the mathematics that people typically think of. For example, I have always been looking into optimisation. I have always done it naturally and I have always been interested in games and optimal strategies.’

At what point did you know you wanted to work in academics? ‘I think this mostly came during my Masters. During that period I consciously chose to hold my internship at a company and to do my thesis on an academic topic. During my internship I felt I wasn’t very satisfied with how I could apply myself and I was also not very satisfied with the way in which people viewed me: it can happen during internships that co-workers just see you as a student and are unsure what you might be capable of. It depends on the company, but it may happen. While doing my thesis I had a desk at the university in the same room as of Hajo Broersma, who is now a professor in Technical Computer Science, and I just felt at home. From then on every following step felt very natural.’ So after consciously making the choice to compare, Ruben never really specifically chose academia as it was the natural fit for him.

Do you have any great memories about teaching at the UT? ‘When I was a student I used to live in a student house and I still had and still have a lot of contact with the people who lived there. The

house doesn’t exist anymore since 2 months back. I knew the people who lived in that house also when I was teaching as a PhD student in 2015. At the time, I was teaching Calculus B for Advanced Technology. One of the students was living in my former student house, so I knew him, but I knew none of the other students very well. I taught them for the whole quartile and there was nothing to be noted, until I visited a house party of my former house. A few of the students were there and I heard them whispering something along the lines of “The beard is here, the beard is here.” I asked the one guy I knew about this and he admitted that was apparently what they called me.’

having to decide which customers to take. Requests from clients, and hence the information on them, only arrive from time to time. Once a request comes in, the driver must decide whether to accept this request or not. In case they do not accept the request, they must wait for the next one, which may very well never arrive.’ Uncertainty in this problem mainly derives from preferences of the driver, who may prefer longer drives over shorter ones (or the other way around). Declining a client may mean not receiving another request for hours, but accepting them may mean the next client, who has a task which is preferable for the driver, must be declined.

Five years later, Ruben attended one more of these parties and a few of his former students from Advanced Technology were also there and could recognise him. ‘When they said they could remember me teaching them Calculus B, I considered telling them that I was indeed the beard, but I eventually didn't.’

‘Uber drivers do not actually have a choice, but from a theoretical perspective this is a very interesting problem featuring 1 server and multiple requests coming in over time which the server must either accept or decline. If you were to know exactly which requests are coming in, it would be very easy to optimise this problem, but the uncertainty lies in the fact that you don’t have this information and you still need to make irreversible decisions. These are the type of problems I am looking into right now. In particular I am very interested problems that tend to be extremely difficult and for which you may not be able to find a solution. By this I mean that any decision may prove to be wrong later on, hence I can never make the correct decision. Suppose we would like to maximise the number of requests we serve, but that the first incoming request takes an hour. Do you serve this request or not? Well, neither is the correct answer. If I don’t serve the request, there may never be another request again and I would serve 0 requests, while optimally I could have served 1. If I do serve

What type of research are you or have you been involved in? ‘I have always been doing research in roughly two different fields: approximation algorithms for combinatorial optimisation problems and game theory. These two fields are actually very much related to one another.’ More recently, Ruben started working on combinatorial optimisation problems with uncertainty and more specifically on so-called online optimisation problems. In these problems, the information about the instances one is optimising over is revealed over time. ‘Think for example of an Uber driver

the request, perhaps every next minute a request may come along that costs 1 minute, meaning that in the same time I could be serving 60 requests instead of 1. This second case could be made even worse by considering subsequent requests coming in every following second and costing one second to serve. Whatever I decide to do, I always make a mistake if we consider the worst case scenario. So I’m basically looking into problems in an online setting for which you can’t really make a good choice. Such problems usually do have a solution in real life though, since in real life more information is available to us. For example, as a taxi driver you know it is almost impossible that no new requests come in or that a million requests come in that only take a millisecond. Incorporating this type of information is a completely new challenge and it’s what I am looking into currently. I could talk about this for hours, but I think it would be beyond the scope of this interview.’

How did you become General Adjunct? ‘The real reason is that I got asked. Usually the General Adjunct of the previous year suggests someone, but I think I heard that the previous board had already suggested me even before that. I’m not sure whether or not that’s true, but I like to think that it is. Besides, I have had in mind to become General Adjunct already for a while, since my time as a PhD student. I never was a board member of Abacus and I thought of it as a lack. It was on my bucket list -so to say- and I am very happy to have been asked, especially since I have been asked after being just one year at the University of Twente.’

What do you remember the most about your student time at the UT? ‘Mostly the fun activities that I’ve participated in and organised, both with Abacus and Vakgericht, the korfball association, which I was a member of from 2004 until 2015. I even was a board member of it at some point. I really enjoyed the Active Member Weekends and the poker tournaments of Abacus. I remember the first one we organised: we had a pretty big cup that the winner would win and then give to the following winner the next tournament and we introduced this rule that if somebody won 5 times overall or 3 times in a row they could keep the cup. I remember that someone had already won the previous 2 tournaments and we realised that giving the cup away wasn’t financially suitable for us, so we added a small prize for whoever eliminated that person. It worked pretty well and we got to keep the cup for the coming editions.’

You used to be an active member of Abacus. Which committees have you been a part of? Is there one you particularly liked and why? ‘I really liked the (A)bac(ch)us and I was chair of it for one or two years. This was back when the drinking room, which we shared with InterActief, was still underneath the Waaier, where the bicycle shed is now situated. It was the first time Abacus and Inter-Actief were sharing a drinking room, since Abacus had no drinking room anymore after the fire in Cubicus. New (A)bac(ch) us members even had to be behind the bar at the constitution drink of Inter-Actief. We also drafted beers

at 3 bar, which is really difficult. Within matters of a second, glasses would be filled and chaining several beers is really complex. Regardless, I liked it very much. It gave me the opportunity to be at almost every activity in a fashion that mattered.’ Ruben has also been a member of the Freshmen committee and the Twick-In, then called the Twick. He was also a member of the Poker tournament committee.

How has it been to work with the student members of the current board? ‘I really enjoy it. I like my fellow board members and I think they are doing very well during the current situation. Everybody hoped it would be better than it currently is. What I do notice for myself is that I can rationalise matters better than when I was a student, although I also notice that all the problems that you see as a student association are actually not that different from the problems you see as a larger company or association. I’m in the Faculty Council and the things we discuss are on a larger scheme, but the type of discussions we have are not that different. Getting that experience as a student is really helpful and relevant expertise to have.’

Is there anything in particular you plan on improving at Abacus? ‘What I would personally like to achieve, is that there is again more interaction between students and teachers during fun activities. Of course this has been difficult the past two years, but what I’ve heard is that drinks used to be visited by employees too. This doesn’t have to

be solely for contact, but I think it’s just good for students and employees to meet each other in such casual setting. It will create unforced interactions and facilitating that would be beneficial for both. It creates an atmosphere in which it is easier to contact teachers and might make things that look difficult much easier. Sometimes there are virtual hurdles that students see and that employees might easily solve if you just ask. A lowkey way of interacting

might help solving these types of issues.’

Do you have any final remarks? ‘I would say: related to what we just talked about, interaction is really nice and good for education, so, if you have ideas about education and your course, contact your teacher about it. Very often, at least speaking from my own experience, I

try to do something with those comments. Immediately talking to your teacher might help you right now instead of only helping students next year. So come to us, come to me, and tell us what is bothering you. We really can help.’

Your Story Text: Emile van der Veer So I was asked to write something about winter. Well, it is possible to write something about that. I could write a bit about why I love skiing, and where I always go to to go skiing (Livigno, it is ducking awesome). But I would rather just write some stuff about what I like, something you can do in the winter when it is cold outside, or just in the summer or whenever you feel like it. I am talking about dice games, and just dice in general. Dice are things that I am interested in for a long time now. You just roll a small clickety clackety math rock and you get a seemingly random number. So I wondered, how random are dice actually? What makes a die a fair die, if they even exist, and how do you get a fair die? All those questions were what I tried to answer in my thesis on high school. Back then, I looked at a few basic things, like why is a die random, and how can we even out small inconsistencies? We start with why a die is random. A die is not random, a die is just almost unpredictable, which is enough for us to call it ‘random’. The more unpredictable rotations

the die makes, the more unpredictable the outcome of the dice roll will eventually become. However, if we make a die that is weighted on one side, we can predict it much easier, since it is now much more likely the die will land with the lightest side facing upwards.

and you will not find a significant difference between fair dice and slightly weighted dice.

Furthermore, we can also talk about the shapes dice can have. We could make fair dice out of all the Platonic solids, since they have maximum symmetry. However, there exist dice with different shapes than just the five Platonic solids. Apparently, you could make fair dice out of any Isohedra, since their symmetry is ‘good enough’ for dice. And since we know that there are groups in the Isohedra-group that have infinitely many shapes, we could in theory make infinitelysided dice.

Thank you for coming to my Ted talk. Bye!

And I could keep on going about these shapes, how weighted dice are, the number configurations of the dice, the material of your die and where you roll your dice on, but I will just get straight to the point. For my thesis in high school, I rolled dice and noted the outcome 20,000 times. And our conclusion was: as long as you take a shape that is close enough to an Isohedra and you do not make it unfair on purpose, it doesn’t really matter,

And that was basically what kept me busy previous winter. Although it might be a lot different than other people’s winter, I quite enjoyed it.

Puzzle: Chess Tactics Text: Martijn Heutinck In this puzzle section there will be 10 chess puzzles. In all these puzzles it is white to move. The puzzles are in ascending order starting with the easiest puzzle up to the hardest puzzle at the end. It is up to you to nd the best move and calculate the variations that follow from it. Good luck and have fun. Puzzle 1: 1k3b1r/1b1r2p1/1Qnp3p/ N3pP2/1p2q2P/4B2R/1PP5/R3K3 w - - 0 1

Puzzle 2: 2r3k1/4ppb1/3p1np1/p3P3/ P2Q3R/1qN2P2/1P4P1/1K2R3 w - - 0 1

Puzzle 3: 8/7R/r4q2/2p1p1kp/p1P1P1p1/ P2pPrR1/5PQP/7K w - - 0 1

Puzzle 4: r4r1k/p6p/5pp1/2p5/ 1p3Q1P/3P1nP1/PP2qN2/1KR4R w - - 0 1

Puzzle 5: 2r4k/1p3R1p/p2qN1p1/4n3/ P3R3/1BP4P/6P1/7K w - - 0 1

Puzzle 6: 3r1k2/2RP1pp1/ pp3b2/7p/8/2B2bPB/P4P1P/6K1 w - - 0 1

Puzzle 7: 8/2pnkppp/pp1p4/ P2P4/1P6/2K2B1P/2P2PP1/8 w - - 0 1

Puzzle 8: 8/5R1p/2rNRnk1/p4r2/ Pp6/1P3p1P/2P3PK/8 w - - 0 1

Puzzle 9: 5rk1/2qnbp1p/3p2P1/3npQP1/1pP 5/3BBP2/rp1N4/1K1R3R w - - 0 1

Puzzle 10: r2qkb1r/pb1n1p2/2p1p2p/4N3/ NpBP2pP/6P1/PP4P1/R2QK2R w - - 0 1

Just Abacus

Things...

A Bridge into the First Year Text: Eva van Laar The University of Twente specializes in project based learning in order to promote real life applications for learnt material. The second project of the first module consisted of multiple assignments based on the physics of trusses culminating in the creation of a model bridge. Trusses are used in civil engineering to create various structures such as bridges and building supports. Students were asked to complete three small assignments about truss physics and then design a bridge that met various criteria set by the “Dutch government”. For instance, the bridge had to be 40 meters wide and leave a 20 by 20 meter space for any passing ships. In order to test the forces on of a multitude of members, also known as beams, of various bridge configurations stu-

Puzzle: Zig-Zag Text: Jorn de Jong

dents were asked to code on Matlab a program that could calculate these forces using what they had been taught that module during linear structures and the rudimentary Matlab skills gained through the programing course.

idea so that it was about to calculate the forces of any stable truss was difficult since deciding where values would have to be placed in the final matrix and how to account for the force of various joints on top of each other.

The code for this project was particularly challenging due to my lack of experience with Matlab as well as the complexity of the assignment. Students were asked as the fourth assignment to create a code that could calculate the forces on all the beams and the attachment points. We had been taught to find these forces by creating a system of linear equations consisting of the horizontal and vertical components of each joint of the truss. Then these equations would be placed in a matrix form and solved using Gaussian elimination. The same basic approach was going to be used in the code however expanding the

Other students commented that the project was also difficult due to its timing since having the deadline right after the exam made both the exam and the project a bit more stressful. There were also complaints of the last minute addition of a poster. Students were asked to build a poster based on their findings however they were told about the additional requirement only a few days before the deadline causing a bit more stress. However overall students found the layout of the project well constructed since completing the 3 smaller assignments provided insight into how to complete the rest of the project.

Puzzle: Hexcells Infinite Text: David van der Linden This is a randomly generated puzzle taken from the game Hexcells Infinite, I couldn't figure out what I had to do next.

jacent cells should be blue. If the number is in a black cell and inside {} then this means blue cells are consecutive. (Does not appear in this puzzle) Instructions: If the number is in a black cell This game is much like mineswee- and inside -- then this means the per, each blue cell has 6 adjacent blue cells are not consecutive. hexes while a bomb in mines- When there is a number above an weeper has 9 adjacent squares. edge it indicates how many blue The numbers on the black cells are below it. (a helping half cells indicate how many ad- line is turned on at the -2-. Sym-

bols -- and {} may be ignored when it comes to numbers above edges) When a blue cell has a number on it there are that many blue cells in a 2 cell radius, this excludes the center cell. (a 2 cell radius is indicated around the blue 9 cell) Now your task is to find an orange cell and tell me with certainty, if it should be black or blue.

Interview: the Board of Abacus

The 54th board of W.S.G. Abacus has been charged in September, and are therefore already a few months on their way. We asked them how they think they are doing till now. Text: Lavinia Lanting and Daan van Kats

What was your favourite day so far? N: I think the second day of the FYASCO. T: I think so too M: That Saturday was indeed a lot of fun E: I think otherwise the day of the CoBo of Inter-Actief from the day of Atlantis. After that we went to turn everything upside down in Inter-Actief's room together with Scintilla, and after that we went to the Vestingbar went with other boards. So I had a good time there. And I also had a meeting with the Christmas dinner committee and one of Linea Recta, so it was a perfect day. What do you most look forward to? N: The end of the lockdown. T: Sad, and what more? N: I'm also looking forward to Christmas dinner and the cantus. M: The ALW, I'm also looking forward to that. N: I don't know what that's like yet M: That's going to be a lot of fun E: The Bata.

T: EWI trip! E: But I also really like to just let people come into the room again without having to count all the heads. N: We don't do that now, do we? T: And the cantus, what a lot of fun activities! E: You've never experienced any of that, Thomas. What will you remember most about your candidate board period? N: An incredibly busy period doing my bachelor assignment including corona. E: In my head it's still just only having meetings. T: The intern and education weekend, that was legendary. N: At that time we weren't even a candidate board anymore! T: Kind of candidate, those were 2 extra days of candidate period. E: I thought it was really nice to see others walking around with a tie like that, and that you always thought 'Hey! You are in the same situation as me, I don't know you,

but nice!' T: And the party in the Vestingbar with a lot of candidate boards. N: Oh where I wasn't there… How did you decide on your board color? N: Well, 53 had chosen the same color as 52, so it had to be better! We then looked back in time and saw all the colors of the rainbow, except orange and purple. If you choose orange, you're practically a carrot so we were left with purple. E: But orange would then have been even better, because carrot = root = mathematics! N: Too bad, we missed that opportunity. E: Purple also has more shades, which we thought would be easy for the shirts. M: Which was still not the case…. T: But we wanted to be original. N: I just liked purple more than orange. T: Yes, me too! Otherwise we would have looked like Stress or Astatine. E: And we didn't want the new students to think that the board can't

choose any color other than blue. And how about your motto? T: That's quite a story. E: I don't think we know that yet N: No, I know, it was very random. It started during policy week in Eindhoven, then it was about Avatar because that windsurfer, Kiran Badloe, had shaved his head except for a blue arrow. We all liked that very much. T: But then we went to GEWIS and there was literally 'Yip Yip' somewhere on a bench where we were sitting. That's the point where 'Yip Yip' also came in. N: We were just yelling 'Yip Yip' a lot back then, and then we thought the bison 'Appa' looks like 'Aba' and then it became 'Aba Yip Yip!' E: At some point we had said it so many times that we couldn't do nothing with it in our policy. T: And now we have the greatest motto you can have. N: Well, you do have people who say 'what a nice motto' or otherwise they say 'WTF does this mean?' E: So it's all because of a windsurfer and the bench at TU Eindhoven What has surprised you most in the last weeks? M: That it's suddenly quiet now E: But just before corona got worse again, I have the idea that it also suddenly calmed down. N: It wasn't because of corona either, but because our policies were pretty much done at one point, guess that was it. T: I didn't necessarily get much quieter. N: But you still have tasks such as working out minutes, which you can enjoy yourself with. I have to actively look for things to do. Assume Abacus had an infinite amount of money. Which activity would you organize? N: Another FYASCO!

E: A culture evening of course N: Or a weekend away M: A ski trip or something? N: Well no skiing, those activities never get enough people.. T: But we have a lot of money. E: Then go to space for a weekend! N: What's so great about that? E: Or we buy a flying bison. T: Insane T: Or an extra floor on top of Educafe so we can expand in the air. N: No, then we just buy Inter-Actief and Scintilla’s rooms.

couldn't find an Overleaf file anywhere, that was very strange. E: Applying for the new bank card.

Describe the new Sjaars in three words T: Lemon tree! E: I think they are excited. M: And of course a lot of Taipan. N: Then in three words “Excited about taipan”

Who is your favourite mathematician? N: Isaac Newton. T: Anti 'vo. M: You really can't say that. T: Then no answer is a better answer indeed… N: That man was a real genius ánd a physicist. T: I'm going to choose Leibniz. E: Euler. M: Fibonacci, I remember him from the first Twentse Wiskunde Estafette where I helped.

Why are you better than the previous board? E: Because we chose a different color than our predecessors. N: And because we don't have corona measures all year round. E: But they couldn't do much about that? N: Secretly I also think that the previous board was better T: Because we get our minutes on time. N: That's not true! E: Because we now have toasted sandwiches in our range. N: I think that's a good conclusion. M: That's a nice one. T: And free curry with it N: And above all because we hand out cake during exams. Were there moments yet where you asked yourselves what your predecessor would have done in your place? N: Registering at the chamber of commerce I think, that was such a mess to do. T: Apparently Luuk didn't even have a template file for the minutes, I

How is your experience with being a board member in comparison to being a committee member? N: It's more fun, especially because you don't have the stress of other things to do. E: It's nice that you can put all your time into it and it's your main job. N: And it's much more relaxed.

Which is your favourite committee to follow until now? E: The Ideaal! of course! T: The FMC, because we get free chocolate every meeting. E: From whom? T: There are so many fail marks being handed out there such that everyone has to take them once in a while, and it is delicious. N: The Education committee is my favorite to supervise, I still see it fairly often. M: I say PixCie! Which new Abacus merch can we expect this year? E: Wait for the DRAMA gift, so become an active member, then you can get one! T: Become an active member, and if you think which committee?, you can talk to me.

N: We had really good ideas for the merch, and then Thomas responds every time with “Who wants an …..?”. T: Look, now I'm getting mad, there's a difference between just selling merchandise and giving it away: then it has to be extra good. If you were a bender, which element would you be able to bend and why? 2 E: I'm the waterbender Everyone: Laughs T: Then I'm in front of the fire E: Thomas is so hot N: Air, I'm blowing everyone away. M: Then the earth remains for me! T: Oh, how original we are again after the See you Sunday drink. Where will the Active Members Weekend be? 2 N, M, E, T: Texel of course! T: We have already rented the whole of Texel, so that will be fine. We had infinite money, right? We have noticed that Linea Recta has started invading Abacus lately. How will you prevent them from colonising our beloved as4 sociation? E: There are only 4 next to me, Sophie, Timon, Emma and Sytze. T: We invite everyone to join a sports association too N: We should just do a Skeuvel versus Linea Recta match! E: But Skeuvel is 53. N: Okay, Klein Verzet then. E: We're more like a Thibats board then. Thomas: As the only person on the board from Twente, how do you plan on keeping the values of Twente up high within your board? N: What are the values of Twente? T: Nice country talk or something? E: Take a minute then!

T: I can only pretend. E: Then you ask Rutger. Thomas: Who of the entire board has the most useful things to say during the board meetings? T: Niels sometimes has good substantive comments about my minutes N: Oh, I am right now? Eline: How are you going to protect the cash this year? E: It doesn't have to be protected3 because money has to roll. T: Then we can finally get a traffic mirror in the room for me! E: And luckily we still have the lovely KasCo who partly protects us. Margriet, Who do you like sneaking money from the most? M: But I don't do that! E: Knaek's 12 euros then. N: Twelve people did that for Abacus? E: And Inter-Actief only had 7 so we won. M: I don't cheat money! I only make good deals and make good advertising. Niels, During the board presentation ….. N: I don't want to be reminded of that. Niels, During the board presentation we saw that you constantly let Thomas lead instead of you. Shouldn’t you be the one to do that? If so, shouldn’t your roles be switched?

N: Thomas needed to get out of his cocoon too, so I gave him a chance. E: Indeed, he needed some training as Vice-President. N: No, our roles are good right now, Thomas makes very nice minutes and is a much better Intern than I could have been. T: That's sweet. Niels: What is it like to lead this so far? N: It's shared leadership isn't it, but yes it is very doable. E: We also have a capable division of functions for that. N: If you communicate well, everything will be fine, that's pretty 4 much my attitude. N: And it's especially fun, even to talk in front of large groups. Do you have any last words? N: We are planning to buy a new TV as a replacement, so a spoiler for now. E: Drink enough coffee so that I can get to the budget for this year. T: And make coffee as soon as it gets below the line! M: Wash your plates! T: So few people do that! E: Don't blame us when there are too few bapao’s, because sometimes they are not delivered. All: “Aba Yip Yip”

Statistical analysis of life expectancies Text: Renske Idzenga In module 5, there is a statistics course and, linked to that, a statistics project. In the statistics lectures, you learn all about the different statistical tools that you can use to analyse a dataset. And in the project, you are free to choose a dataset, think of research questions and answer them using the tools you learned. Also, we needed to do regression analysis using another dataset. I was in a group of 4 with Nynke, Leanne and Ylona.

test we found that indeed, both in 1960 and in 2019 women live significantly higher than men. In our second research question, we wondered if there was a difference between the life expectancy of 2000 and 2019. These years are quite close, looking at the range we had in our dataset, but that made it more interesting. I guess most people know that the life expectancy in 1960 was way lower than now, but in more recent years it is not as obvious. But we did find that the life

expectancy in 2019 was different than in 2000, where it is higher in 2019. In the last research question about this dataset we compared two countries: Bangladesh and the Netherlands. According to the Human Development Index, the Netherlands is the 8th developed country while Bangladesh places 133th. We compare them over the life expectancy of the 21st century, so from 2000 to 2019 again. This

While looking through the sites with data, we found a dataset on the life expectancy. This piqued our interests, as you often hear claims about life expectancy, like: women live on average 7 years longer than man. Or: the life expectancy now is longer than 20 years ago. And we of course expect that there has been statistical research done on these claims before they were made, but in this project we could check if the claims are actually true and based on data. The dataset has all the life expectancies of several countries over a timespan of 80 years. Not only did we have the combined life expectancy per country, but also the life expectancies separated for males and females. These were all separate datasets that we first had to merge using Python, but after that we could start with the statistical research. We had thought of three research questions and we answered all of them using a significance level of α=5%. The first question was: Is the life expectancy of females in 1960 and 2019 significantly higher than the life expectancy of males? Luckily this data was approximately normal distributed, so using a Student’s T-

data was definitely not normally distributed so we had to use a nonparametric test. Here we found a p-value of 1.451*10^11, which is really small so we could conclude that there is a difference between Bangladesh and the Netherlands in life expectancy. In the regression analysis part, we had another dataset: the urban population across the same countries and same timespan. We wanted to know whether there is a correlation between the urban population and

the life expectancy of a country. Our reasoning behind this was that if a country has a high urban population, it is relatively prosperous. Then there would be a safe living environment and accessible health care, which both contribute to a higher life expectancy. To answer this research question, we made scatter plots of the urban population against the life expectancy and residual plots after creating a linear regression model. Here we show the plots of 2000, as they had the most linear regression.

We saw in the scatter plot that there is an upwards trend and from our hypothesis test we could conclude that there is correlation, but that the correlation is very low. So it might be that a higher urban population correlates with a higher life expectancy, but there are probably other variables in play.

Review: D.S.V. De Skeuvel Text: Luuk van der Werf Since my first year here in Enschede I am a member of D.S.V. De Skeuvel or just Skeuvel. Skeuvel is the ice skating association of Enschede. This is perfect, because there is a very nice professional ice rink

just next to the campus. From October up until March you can skate every Monday and Thursday evening. Since you only pay contribution once per year, this is a great steal. You might think: ‘Skating is very hard, this is not for me’. This can of course be the case, but the training groups are based on your level. This means you train with people that have the same level. Every training group has a personal trainer. With this trainer you focus on the things you can easily improve. In this way you make a lot of progress quickly. I also started in the lowest training group, and after three years of progress I can know skate quite well, if I say so myself. At the end of every winter season there is a big tournament for all the members to show of their progress. Here you race against people of your own training group to see who is the fastest. Of course you cannot skate the whole year. Once the temperatures rise you can do multiple other sports at Skeuvel. There are cycling trainings, as well roller skating trai-

nings. Also, there are dryland trainings. Here you train on the skating stances, but than on land instead of on ice. Skeuvel is also an association that organises activities next to sporting. There are monthly drinks, and they have a committee that organises activities. Next to that they organise multiple trips abroad. You can go to Italy in the winter to skate, and to the Ardennes in the summer to bicycle. If you want to do a sport that is not so standard, and at which you can make a ton of quick progress, Skeuvel is the place for you!

Review: Tim Burton's A Nightmare Before Christmas Text: Lavinia Lanting This much needed vacation is finally at our doorstep and hopefully, with a bit of luck, I’ll be able to be home for Christmas this year. I know my mother for one would certainly appreciate that and I have to admit I did miss that grandiose celebration I would usually have on the 25th of December with my parents, aunt and sister. Speaking of Christmas, for those of you who have been reading the Ideaal! more or less on a regular basis, you may recall an editorial I wrote some time ago for another winter edition in which I talked about how my sister and I have this ritual we carry out every year: the 23rd of December we’ll head out, just the two of us, to the Christmas market in the city centre of Milan to buy the final missing gifts for our family and to have a day all to ourselves. Nowadays this is also a good excuse to catch up in all liberty and to treat my little sister to whatever she feels like having whilst out and about. This is though not the only tradition we have around Christmas.

As far as I know, a lot of people associate Christmas with watching ‘Home Alone’ or ‘Home Alone’ or with the reruns of all the Harry Potter movies, but that is not quite the case for me. One faithful Christmas, when I was about 7 years old, making my sister 5 years old at the time, my father gifted us, among other things, with a DVD of the Oscar nominated for ‘Best Visual Effects’ movie ‘The Nightmare Before Christmas’ by Tim Burton. Immediately intrigued by the cover of the DVD, on which the protagonist, Jack Skellington, very poetically stands as a shadow in front of a full moon atop a creepy looking hill in the middle of a field of Jack o’ Lanterns, we just had to watch the movie as soon as lunch was over. Tim Burton’s ‘The Nightmare Before Christmas’ follows the adventure of Jack Skellington, King of the pumpkins, and important inhabitant of Halloween Town as he struggles finding the will to organise yet another Halloween. The skeleton finds himself having lost the passion that was driving him until that point and ends up by accident in Christmas Town while looking for himself inside the forest of festivities. The novelty of Christmas, a festivities he does not know, seems to breathe new life into the skeleton, who becomes determined to organise Christmas himself: he even kidnaps Santa Claus and hands him to the Boogie Man in order to achieve this. But of course not everything turns out as wished and along the way Jack rediscovers himself, his relationships and his passion for what he does best: deliver a good scare. I’m not certain exactly why, but my sister and I immediately fell in love

with this movie. Maybe it was due to the huge variety of unique and fun characters, maybe it was the catchy music, maybe it was the intriguing storyline about the King of the Pumpkins losing his passion for what he stands for and rediscovering himself and his occupation after ruining Christmas or maybe it was the beautiful stop motion animation that made this movie so iconic for us or maybe it was more simply the fact that Christmas is and always has been for us as Italians one of the most important and joyful festivities of the year together with the fact that my sister was born on October 30th, which meant Halloween has been for us also always reason of joy and party and this film was a perfect blend of the two festivities of the year that brought us together as a family. Since that one faithful Christmas, our celebration is never complete unless we watch this movie all together. So while I can’t say that Tim Burton’s ‘The Nightmare Before Christmas’ is a lifechanging movie that will blow your mind away, if you are looking for a light-hearted, music filled cartoon about rediscovering yourself and your relationships in a festive context, you might just want to join me and my family this Christmas in watching ‘The Nightmare Before Christmas’ while cosily sitting all together wrapped in a warm blanket as (hopefully) a white coat of snow forms just outside of your window.

Puzzle solution: Rectangles in a square Text: Jorn de Jong The puzzle was about squares and rectangles. For 2, I already showed that it was possible. For 3, it is not, since one rectangle needs to touch two corners of the square, hence the other 2 need to fill a rectangle with ratio 1:2, which is not possible. 4 is not possible by the same kind of reasoning. By splitting one rectangle into 4, like in the image below, we can fill the square with n+3 rectangles, if we can do it for n.

By adding 4 rectangles to a square,

like in the image below, we can fill the square with n+4 rectangles, if we can do it for n.

tangles, and also with 8,9 and 10 rectangles. Since now we have 3 consecutive numbers, we can do it for all numbers bigger than 8. The only one left to check is 7. 7 is possible, but it’s hard to come up with. So it is only not possible for 1, 3 and 4 rectangles.

With 2 rectangles, we already showed it was possible. This means we can do it as well with 5 and 6 rec-

Puzzle solution: What's the PIN? Text: Martijn ter Steege Solution: 23, 37, 53 and 73 are the only prime numbers that consist of two

separate prime numbers. Mimi says she knows the code, so her numbers rule out three numbers of

Lana. This could be 27, 57, 72 or 75, only 72 is even. The code then has to be 7253.

Dies Cake Reviews (continued) Apple Pie by Sem Geerts

en ty, looks s e ta , ic b s s la C e v a lh ood. The hazelnhu.ts Wouldwithout hazuein g r a nice touc re a bettePr, still can’t/1 0 nut : le pie. 7.5 The app app althougleh pie was dec unneces the nuts w ent, ere sary, gra de > 5.4 Delicious, but the nutli things took away from ke experience 4/5 the 24

Rocky Road Brownie by Leanne van der Meer

t nice, ry e o v l s a w ie a n w ro e B t ri o v dry it a b f a s s a w y a it r e t v m e w o o h s Wa oconut, n /10 ter! a w d d a e m ti t x e n 0 c o s of ar 1 g u s h The brownie t muc asted very mu c h u o o colate, which ch like 6.5/10, c w a s ld be better, a bthe texture was a bit onice, but ecause it was ff, likely bit dry, great i n th open air i n marshmellows Educafe for a long etim e 7/10 sqrt(pi) by David by David de Haan

Fucking nice!, Luuk 8.5/10 tasty, nice contra the frosting, n st with i c ely spongy 9.5/10 good t e x ture, tasty nu 4.5/5 stars t s , just goooood. Best cake I ever had ~ Tubantia Good taste ~ New York Times msay Tha ~ Gordon Ra ve lo e th e st ta n ca u Yo tas t wa Bakt swe ty, s v It changed my Life ~ Heel Holland et, not ery Great cake, ta Ma too stes good. Th rgr a m i s e cree s p ecially nice. R iet ating 4/5 Soft and just acidic enough. Really nice. Blueberry Lemon Cake by Anne Meulenkamp

8.5 out of 10 ake is perfect, c Very Yummy : is te s ta e im L Right amount P ely glaze on topo.uld v lo , th o o m s blueberries of Blueberries only on bottom, c be more spread TASTE GREAT! 25

Monchou by Marjolein Bolten & Sanne Oude Veldhuis

, The moncho g in h s e fr re , ty s ta , 0 1 / 8 utaart was ve t is ry o n m i it c b e, Thx, Little J a . 3/Pi Amazing! e. ic n s te s ta ll ti s rt a ta u The moncho Thx, Little J The monchou which made itaart was very stuck a tasty, whentImessy to get out, butt itthe bottom managed to g as very et it off. 7w .5/10 Lime Pie by Anouk Beursgens

SubLIME ;)) 53/52

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reen, and green is Also the good p Much Nice good yes henc e this ipeiewas fantastic, ly my fav was definiteVery tasty cake, fresh as wel. I am ourite. ! y curious about the recipe. t s a t g n Fucki /10 Rating: 4.5/5 10 on top that did The lime pie had some creaman fell off, but not really taste like anything amdaz ing 8/10 the two layers beneath were The lime pie had a great foundati V e on, Esp ry t bu t th e to p ha d a weird taste. eci ast foundation grade >>> 5.4, ally y w i the th a Top part grade = 5.4 bas nic e w e te as xtu am re azin g. 26

Tiramisù Cake by Lavinia Lanting

ouch t e c i n , r u o v a Chocolatepleycflan. Too soft to eat lavour 9/1/010 with the e paper towel. 8/10 F e of use 3 52/60 from th Eas pleasure sual i V 8.5 out of 10 o spongy) to t o (n rs e g in v e g n la t a Gre flavour Love the chocolaate nno… Missed the Dis tro at e to t n ie n e v n o c s o m Due to cream not the "Other"

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Thanks for all the delicious cakes!

What is better than one pie? Tau 10/10 , e c i n d e t tas urprise s e i p l l a Not this was a s es of pie, for mesome free slic reason why, d he for us, t s i y a d I enjoye rth made pie i b r e us h s Abacume members out to Sytze Horj So out h s a h t i I end w I really liked all PI’s!. Yes I tasted em all. Especially the tiramisu pi was deth ious and the lime pie was SubLIMlic E

Puzzle to win a wireless powerbank 1

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DOWN 1 The museum that became a long-term partner with ASML. 2 A wafer is made of this material. 4 ASML’s supply chain has this many tiers. 5 Name of the event where ASML created the “You Gave Me Wings’ project. 6 The family of optical metrology systems produced by ASML. 7 First name of ASML’s CEO before Peter Wennink. 10 One billionth of a meter. 12 ASML bought this company to develop light sources for EUV machines. 14 Name of our largest customer in the United States. 15 Abbreviation of Supply Chain Management. 17 Thin membrane which is used to keep out particles. 19 An ASML-organized event for those who love music performance, called ‘ASML ...’. 21 Last name of the co-founder of Intel, which is now the name of semiconductor scaling. 23 One of the 3TG minerals that ASML uses in manufacturing.

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ACROSS 3 A projection technology used during the chip fabrication process. 8 The country where an acquisition by ASML took place in July 2020. 9 One of ASML core values. 11 Name of the football club that is sponsored by ASML. 13 Most of ASML’s customers are in this continent. 15 ASML operates in this industry. 16 This Dutch company makes both cars and parts of ASML systems. 17 Name of the first machine launched by ASML. 18 The solution to measuring imaging performance on wafers. 20 ASML was founded in this type of building. 22 A program by ASML that aims to prevent unnecessary waste by remanufacturing used system parts. 24 ASML is the world’s only manufacturer of lithography machines that use extreme ... light.

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Send an email with the correct answer in the subject line to campuspromotion@asml.com by April 2022. Each month until then, we’ll randomly select one correct answer from those we receive. Winners will be notified via email. You can only participate once in the draw. The results are not open for discussion.

Curious to learn about our opportunities for students? Visit www.asml.com/students