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© nqo

Lab Christmas Calendar 2022

Every day until the 24th (maybe not on the weekends...) we will post a small, lab-themed challenge here. The challenges will also be sent out on email, if you want to recieve the emails, let us know by emailing Nina 🤶

If you have solved a challenge, you can email your solution to The Calendar Team on (put the date in the header, thanks, and do mix dates 💖). Answers to questions given between the 1st and 8th of December are accepted until Sunday the 11th. Answers to questions given between the 9th and 15th are accepted until Sunday the 18th and so on.​

Correct solutions are uploaded on the webpage at some point after the answer-deadline is over. We promise to do our best! From the correct answers we will draw a winner of the Christmas Calendar 2022 - and maybe there will also be a prize for the person with the most correct answers. Time will tell 🎄. We have not yet handed the prize to the winner of the Calendar 2021, but he will probably received it over Christmas this year, because it has been gathering dust for some time now. 🎁

Please feel very free to forward this email to colleagues, friends, your grandma, ... If you get this email 2nd hand but would like to receive a lab-themed challenge in your mail-box every day, directly from the source, just get in touch! Questions can be emailed either to the Calendar email or directly to Nina.

Correct solutions are uploaded on this page at some point after the answer-deadline is over. We promise to do our best to be fast.

Please feel very free to share this with colleagues, friends, your grandma, ... , and to sign up for the emails. Questions can be emailed either to the Calendar email or directly to Nina.

We hope you enjoy the puzzles 💖

They are based on Ian Stewarts amazing books  Professor Stewart's Cabinet of Mathematical Curiosities, Professor Stewart's Hoard of Mathematical Treasures, and  Professor Stewart's Casebook of Mathematical Mysteries  Carl-Otto Johansen and Arne Hansen: Hovedbryderen – Politikens håndbog i hovebrud 3.

Anyone looking for gift-ideas? Then start with Professor Stewart's Cabinet of Mathematical Curiosities.  📚


(Drawings are normally made by Nina and subject to normal copy right)

1st of December (based on a true story!):

The postdoc (we know her from the two past years when she was still a PhD student. She has leveled up in between. She dislikes crossing cables.) didn't even look up from her papers when the PhD student (we also know this guy. He was the star of December 14 last year.) entered the lab. Instead she sighed into the pile sheets, which were filled with scribbles.
'Will there be a calendar today', the PhD student demanded cheerfully.

'I don't think I have time this year', the postdoc muttered, 'I have to give the lecture in an hour, and I'm stuck in this calculation which makes no sense...'.

'I made a calendar for the lab', the PhD student announced undisturbed, and held a box in front of her.

It was a red cardboard box. He had written a big number 1 on it. It was filled with candy (you see it in the header of this page!).

'This is for the 1st of December', he said happily.

'Maybe I'll make a calendar too', the postdoc said hesitantly, 'but it will maybe be a bit different from last year. I will for instance only upload answers on weekends, and maybe there will be no weekend entries...'

Then she pointed at her sheet of paper.

'Look, my problem is this. This is supposed to be a positive whole number between 0 and 10. But instead I get...

4      9.

Makes no sense.'

The PhD student looked at the sheet. Then he looked at what was before the equality sign.

'Huh, how do you get rid of that?', he said and pointed at a standard mathematical symbol.

'.... Well, I don't, I think I missed it.' The postdoc said a bit perplexed, then she beamed at him 'Oh wow, thanks a lot! Don't tell the students that I forgot a ...'

'I promise, now go make that calendar!', the PhD interrupted her.

'First I give the lecture, OK?'

What standard mathematical symbol was the postdoc missing?

© nqo

2nd of December:

'I got them!', the postdoc exclaims as he bursts through the door, holding up a chain of cable ties that he 'borrowed' from a generous neighbouring lab. Wait, is that... The same chain as the one his colleagues played with on December 1st last year?
'Perfect,' the former-bachelor-student-now-lab-helper (HiWi) says happily.
She is standing on an 'elephants foot', organizing some cables above the experiment table.
'I actually pulled the cables through here, so I don't know how many I need, though', she adds and shows him.
'Maybe I just need one. Or two. - Or actually three.'
'Four would be better,' he says 'but you could also put on there and one over there, then we need six. The chain has 23 cable ties.'
'Ok, let's just take them one by one' she suggests.
'OR!', the postdoc says, 'I open these two cable ties, and then you can have any number between one and 23.'
'Oh, impressive!' the Hiwi says, though she knows that she will have to take a chain of length N apart anyway.

Which two cable ties does the postdoc open?

© nqo

To clarify, if the postdoc opens the 2nd cable tie, he can give the HiWi one open cable tie. He can also give her two, because he has the one he separated from the rest of the chain, and the open one. And he can give her 21 (23 minus the open one and the separated one), 22 (21 plus the open one) or 23 (21 plus the open one and the separated one.)

© nqo

3rd of December

The professor enjoyed a relaxed Saturday. Coming into the kitchen to pick up a nice cup of tea which had brewed long enough, he found one of his daugthers at the kitchen counter. With a box of matches.
'Hey, you are not playing with fire, are you?', he asked, his tone slightly nervous.
'What? No! Duh' she answered, looking up from the box of matches, 'How old do you think I am, nine?'
She rolled her eyes, but the professor didn't notice, instead he looked at how she had lined up the matches.
'What are you doing, then?' he asks curiously.
'So, I saw on TikTok. You have to get the cow-poo out of the shovel. You can only move two of the matches. But I thought it was too easy, ...'
The matches are shown in the drawing. She had used a raisin to create a lifelike cowpoop.
'That is easy!' the professor says, and moves two sticks.
'Nono, you cannot just turn it upside down, the cow-poop is really sticky, it will not come out like that.',
'Uh, okay...' the professor now had to think a bit about how to solve the puzzle.
How can you solve the puzzle

Bonus question
'But it is really simple!' his daughter continued talking, 'So I thought I'd make a puzzle that is more difficult'.
'SO!', the professor had now figured out how to get rid of the cow-poo, and looked at the other matches she had lined up.
'So, what will your puzzle be?', he asked her.
'I was thinking of two squares, and then you can move two sticks and have to...' She showed him, 'what do you think'.
He looked at it for a second, and then they said in unison:
'That's too easy'
'I cannot think of something more challenging.' she sighed.
'How about...' the professor started. 'Hold this one, ... So!'
'I see!' she said, 'You have to make three squares and two triangles, each with sidelength one match. Using nine matches'
'Yes, how is that for more challenging?'
'I think it'll go viral,' she said.

© nqo

4th of December:

Somewhere in Bonn two postdocs from different fields meet at the dining table of their shared flat.
'How was the game last night', the physicist asks.
'Super cool, I really liked it, actually,' the neurobiologists beams, 'I was a bit skeptical, I mean, I didn't think DND would be something for me. But listen, you should join next time, then we do it with more people, it'll be supermuch fun. I think the guys will cook something nice, though I told them we cannot fry anything in our flat, ...'
'Sure, I'd love to!'
'The only problem is that you have to roll the dice to find out what your skills are.'
'Haha so if you roll badly, you get to be dumb as f*ck?'
'Eh, luck is a bitch...'
'Tell me about it.'
More things can of course be determined by dice, and the postdocs get some dice out to already determine what the physicists will play as next time.
'We start with how cute you are.'
'Really? Is that in there?'
'Sure! Or it is called charisma, but it's the same. Hmm, yesterday we had a dice with twelve sides,' the neurobiologist says, 'that of course gives a bit more opportunities, do you have a dice we can use for that? It should of course be equal probability for every number between 1 and 12.'
'I do, actually,' the physicists finds the cube.
'That's a funky dice!'
'Yes,' the physicist agree and rolls one normal dice and her special dice.
'That's a bit dissapointing.'
'Don't worry, maybe you are wise, roll again.'
'Nah. What's next?'
'Dumb as f*ck'
'Hmm,' the neurobiologist looks at her sheet as the physicist rolls again.
'Whatever the next is, it also doesn't look so good...'
'This was just a test. You can start over.'
The special dice work together with a normal dice such that there is equal probability of getting any number of eyes between 1 and 12. What is on the sides of the dice?
© nqo

5th of December:

This entry is late - the Calendar Team is sorry for this, but simply forgot to also upload on this page. You can sign up for the calendar emails for earlier riddles 💖 Now to the riddle!

The HiWi and the bachelor student are keeping the lab in order, collecting loose components lying on the optical tables.

'I think I am a bit messy,' the bachelor student says, looking at her collection of posts and the pair of lenses which did not actually work out in the end. She also has left a few cables for an oscilloscope lying around.

'Oh, come on,' the HiWi giggles, 'you call that a mess?'

The HiWi has indeed collected a lot more posts, clamps, screws, optics pieces, fiber caps, used lens cleaning tissues, a detector card, a few T-pieces for BNC-connections, a lot of sticky notes, a cent, an empty battery, some cable ties, a hex key, a few screwdrivers, ...

'I need to practice my mess,' the bachelor student says, 'now look at this little game.'

She puts the six posts 1 inch posts she has collected together.

'So, you have to turn this shape into a circle'

'Like this?'

'Yes, that is what it has to look like, but you cannot move like that.'


'No, one move means that you need to move a post a post until it rests between two other posts. Like roll it.'

'Oh... Hmm, like this? One, eh.... Oh yes, it will work, two, three.'

'Very good!'

'That was not so easy!'

'No, but you were very good' the bachelor student says happily.

'I think so too!' the Hiwi agrees cheerfully.

© nqo

This is the starting position, an example of an allowed move, and the final position.

© nqo
© nqo
© nqo

6th of December:

'You have two seconds?' The former-bachelor-student-now-laboratory-helper (HiWi) asks.
'I have to teach in literally two seconds,' the postdoc says (this is not entirely true, but she is indeed short on time for turning on the projector and getting the microphone working).
'I have the power-distribution circuit here, but the documentation is not soo good. How many components do I have to put where?'
'Oh, eh, I don't recall exactly. There are only voltage regulators and capacitors in the first part that power the board.'
'Okay. How many? If you just tell me how many of each... '
'And then you have the second part which powers the amplifiers. Eh... You have 11 components if you count voltage regulators and capacitors. And 9 components if you count all voltage regulators and all resistors, and uhm...'
'Okay.' If the HiWi wonders why the postdoc knows only sums he hides it well.
'And the sum of capacitors and resistors is 14! Now I have to run, sorry, we can talk about it afterwards,'
'Don't worry, I got it.' the HiWi says cheerfully.
'Eh,' the postdoc says, maybe a bit surprised that anyone got anything from her weird numbers.
'... great, super, you got it!' The last words she shouts as she dashes from the room.
Then she crashes back into the room 'Hey, you are supposed to be in the lecture!'
'Yes, but I still have time to solder a feeeew more components. Now go make sure the people on zoom can hear you.'

How many voltage regulators, resistors, and capacitors do the HiWi need for the soldering project?

© nqo

7th of December:

The PhD student has gathered optics on an optical table. He plans how to best build a new part of the optical setup.
'You don't need this right now.' The bachelor student tells him, as she picks up the powermeter from the table.
'Eh, no, not right now' the PhD student says absentmindedly, and continues
'The fiber outcoupler comes first, then a mirror. Lens 2 comes 150 mm after lens 1, the AOD is 100 mm before the iris, lens 1 comes 100 mm after the shutter, the dichroic mirror is 200 mm after lens 1, and the iris is 200 mm before lens 2. The waveplate is just before the dichroic mirror. Only space limits the distance between the fiber and the mirror and the first element, and... that's it.' he trails off, looks thoughtful, then he nods in satisfaction.
'What?' the bachelor student says, 'that was not for me, right?'
'Huh, what?' the PhD student looks confused, then he bends over laughing 'hahaaha, no, not at all. That was just for me'
'Okay, because it was a bit hard to follow' the bachelor student laughs.
'Really? Maybe you are right.'
'Well, I could for sure work it out if you'd say it again,' she says with confidence.
'I bet you could!' he agrees, 'but maybe it is easier to go from one end.'

In what order should the optics pieces be placed?

© nqo

8th of December

'Wooooow', the visiting professor marveled when she saw the ytterbium MOT (you can also enjoy the sight, check the picture gallery on our webpage!). 'It looks amazing, you guys! So much better than yesterday!'
'Yeah, it's pretty good,' the PhD student said modestly.
'No, it is GREAT!' the professor beams, 'You... I leave you alone one minute, and then you make this progress! And you didn't even send me a message!'
'Haha no, we wanted to see you reaction!' the PhD student smiles, 'But actually, after you left yesterday we went through the parameters again and found a signal which was better. And then we could align much better.'
'Wow, and you really did well! It must be ten times as many as yesterday?' the professor has turned again to look at the glowing blob.
'Actually, a facto nine, yes! But I think we can find at least another factor five or so.'
'You think so? This is already excellent! But then I'd say that it looks very promising!"
'Yes! Now we are as far above 1*10^9 (one-ten-to-the-nine) as we were below 1*10^9 yesterday!'

How many atoms did the ytterbium team have yesterday, and how many atoms do they have today?

© nqo

9th of December:

The Nonlinear Quantum Optics group went to the Friday colloquium today.

'But let's start somewhere else', the speaker announced, as he changed to the next slide. A friendly-looking grasshopper appeared.

'I have found', the speaker said smiling, as the audience laughed in surprise, 'that including some animal in my talk makes people remember it better.'

The grasshopper was part of a problem: It makes a jump of length d, starting somewhere on a lawn. Now, the question was: what shape of lawn is optimal for maximizing the probability of the grasshopper landing on the lawn again. This is not a trivial problem, and not the topic of the Calendar today, yet the I think you should take a look at riddles turning into math problems!

The talk was on dipolar quantum gasses. Also extremely interesting.


As the group leaves the room, the head of the Calendar Team is deep in thoughts. 'I have to change my calendar plans,' she tells the HiWi. 'The riddle for today is not good for today, it doesn't feel right. I want something with grasshoppers!'

'Maybe do something about someone who hears a talk', the Hiwi student suggests.

'That's not so bad either...' the head of the Calendar Team says thoughtfully, then she enthusiastically asks 'What do you remember about the room?!'

'Eh... It was the normal colloquium room. It has, I don't know, 100 seats.'

'Let's say 200. And let's say that there is the same number of seats in the middle part and in the back part.'

'I think that today six more people sat in the middle part than in the back part.'

'And let's say that the people who sat in the front part and the middle part would exactly fit into the seats in the back part. So if no-one sat in the back part, I mean.'

'But someone sat in the back part. Let's say that all the people who sat in the back today would fit into the empty seats in the front and middle part.'

'We need some reference to real numbers now, I think,' the head of the Calendar Team was now finding it a bit difficult to keep up with the HiWi. 'I suggest that we say that in the front part of the room the filled seats were one eight of the total number of seats in the room. Plus three.'

'Are these numbers a bit high?' the HiWi asked, doing the math in her head.

'Maybe a bit high - but they should have been that high, it was an excellent talk!' the head of the Calendar Team said, smiling as she vanished into her office to scribble some notes on this.


How many people were in the front, the middle and the back part of the room.

© nqo

10th of December:

'Can you come in here?'
'What is it?' The professor gets up from his chair, takes a quick glance at the text he had been reading, shrugs - the poster with suggested bachelor projects for next year can for sure wait until Monday - and walks to the other room.
'So?' he asks his younger daughter, who again is occupied with match sticks, 'what is it?'
'So, you know last Saturday,' she answers, smiling and gathering all the matchsicks that she had spread over the table to a pile.
'Yes, viral video and so.' the professor already pulls out a chair.
'Yes, and now I have a new riddle.'
'Maybe you will solve it with me?' she beams.
'Absolutely!' the professor sits down 'Have you already solved it? Is it too difficult for me?'
'I think you will manage.' she smiles cryptically.
'So you already know how to do it?'
'It is like this, a big triangle with six nine smaller triangles of 18 matches. Now, remove three five sticks to make three new triangles of the same size'.
'Easy!' the professor removes the five sticks.
'Yes, this is also what I did.' his daughter says cheerfully.
'Great minds think alike, you know'

What did he professor do?

Bonus 1
'Now, put them back' the daugther says.
'I'm not done?'
'There is another one on the same set.'
'Move five again, but now we want five triangles with the same size.'
'Hmm,' the professor says thoughtfully.
'These games are really popular on social media,' the daugther informs her dad as she starts peeling a mandarine.
'Okay,' her father says a bit absentmindedly, 'Oha, like this!'
'If you were young you could also do this on videos', she says proudly.
'Hey?' the professor is not sure if he was just complimented or insulted or both.

Bonus 2
'Okay, now you have warmed up!' she goes on undisturbed. 'This is where I am still puzzled.'
'Show me!'
'This is like an equation!' she arranges the matches. 'And it has to give 130. You can only move one stick.'
'Oh. Hmm.'
they sit a bit in silence.
'You must change one of the numbers somehow,' the professor starts, but he is interrupted.
'Are you still doing the triangle??' the older daughter has entered the room. 'You didn't get any further?'
'Hey, don't talk like that to your sister,' the professor says.
The girls exchange a glance. 'It wasn't for her' 'It wasn't for me,' they say in unison.
'No, we have an equation now.' the young one says to her sister.
'Oh.' the older sister leans over and looks at the problem. Then she smiles very happily and pulls out a chair too. 'We can solve it together. I think you have to change one of the numbers somehow. or maybe the symbols. Give me a mandarine too!'
'You don't need me here, do you?' their dad asks.
'Yes we do.' the daugthers answers resolutely together.

© nqo

11th of December:

The postdoc is an enthusiastic runner.
Today she went running in the forrests near Bonn with a PhD-studying friend. He normally works on animal vision.
'So it is quite difficult to simulate what the mouse see when we only have this super limited information about what the eyes actually look like.' he says, jumping over a fallen tree'
'I see,' the postdoc gasps.
'But maybe my model and the data from those exeriments I told you about, where they just observed where the mouse is looking. Together, I mean, this can maybe tell us what the eyes actually look like! Huh, we have been here before. Okay, lets check the map briefly,' he stops on the narrow track.
'Phew, we already... went quite far!' the postdoc gasps, thankful for a brief stop. 'Wow, it was muddy back there!'
'Yeah! And where we had to walk on the fallen tree to cross the little stream... Or where we had to balance on the branches' the PhD laughs as he is looking at the exact route they have been running.
'And where we had to jump over the water!' the postdoc still feels that adrenaline rush.
'Quite a good route...'
'The best thing is that we didnt' cross our track even once until now!' the postdoc says. If you recall from last year, she dislikes crossed cables and also crossing running tracks.
'True.' The PhD student looks up from the map, amazement in his face, 'And we crossed the stream basically everywhere possible! Look'
'Wow we were, like, everywhere!'

The runners crossed the water and the big road along the red lines. The have now returned to a point where their tracks will cross for the first time in order to get off the map. Where are they and what route did they take? I didn't draw the trees and the forest on the map, and the map is not to any scale. You have to imagine it :)

© nqo
© nqo

12th of December:

The master student has been working on a theory projects for some months now.

The postdoc enters their shared office.
'Does it work?' he asks curiously. The master student sighs.
'Yes, I feel stupid. I found the mistake, just as you said.'
'Mistake? I didn't say anything about a mistake.'
'Yes, I had overlooked another symmetry. You said that there could be more, right?'
'That isn't a mistake.' the postdoc says with a dry smile 'That is progress.'
This cheers the masterstudent up.
'Well, right - and it is much faster now!' he adds excitedly 'if we can find a bit more optimization we are as fast as the basic code.'
'Where you don't have the full system' the postdoc asks to clarify.
'That's right. Yesterday the full code was seven times slower than the simplified code - or so I thought. But with the new symmetry I gained three minutes on my run-time'
'Wow,' the postdoc says, clearly impressed. 'that is really good! I mean, you will not beat the simple program, but every minute...'
'Well, yes, I also had a look at the simple code, and actually it is not as fast as I thought, I was not timing it so smartly. So it is actually three minutes slower than I orignially thought. I can probably optimize it, but I didn't bother so far.
'Haha you should have a look at all my code, I think.'
'Maybe I will when I'm done. But still, actually the code of the full system is only four times as slow as the simple model.' the master student feels way better now, and laughs as he points to his script. 'Look, the impotant thing was this for-statement...'
'Sure, but show me the real code. I want to see your new code symmetry!' the postdoc grabs a chair and pulls it to sit next to he master student.

How fast is the code for the full system and for the approximative system?

© nqo

13th of December:

​The master student is doing some data-analysis. It is cold and dark outside.

The PhD student peaks into the room. He is wearing his winter gear for biking in the biting cold.

'It is super late, are you still analyzing data?' he asks her.

'Hmm?' The master student wrestles her eyes from the code. 'Oh, yes, it is actually pretty late... yeah. Yeah, I just want to make this work, then I should go home.'

The PhD student smiles sadly. 'Well, that's a dangerous thing to say.' He knows this from experience.

'Why are you still here?'

'Oh, I was briefly home, I just came back right now. I'll finish my talk tonight!'


'What is your problem?'

Well, the problem can be condensed to this: The master student works on some imaging. She is expecting a four-fold symmetric pattern, so therefore she has cut her image in four pieces and rotated them such that she can put the four pieces of her image on top of each other to increase the visibility of her signal. She took some data long time ago and analyzed it with some code that was then modified and only versioned too late. Therefore she doesn't know which of the four pictures were located where, and how they were rotated. The only thing she knows was that she only had one bright pixel (plotted in black) in each row and column.

You see the data below.

'But I'm sure I can figure it out, I just have to look carefully.'

'I think you can do it, too!' the PhD student says and heads off, determined that he will also finish his PhD talk tonight.

© nqo
© nqo

14th of December:

The bachelor student on the fiber-cavity-optomechanics project is sorting some fibers when the PhD student enters carrying a large box.
'Oh, what did we get?' the bachelor student asks curiously.
'Lots of new things! I ordered more fiber rolls.'
'Also some for me?' the bachelor student does not have any real need for fibers, but more is more.
'Yes, actually, but that did not arrive yet. This package has some experimental stuff I would like to try out.' the PhD student smiles mysteriously.
'Oha,' the bachelor student peaks into the box. 'Looks like normal packages of fibers,' he says shrugging.
‘Yes, but I’ll try with different core diameters now.’
‘Yes, I got a roll with two micrometer core diameter, and a roll with four micrometer. And then I got one meter with one micron core diameter.’
‘Oh, wow!’
‘Yes, I think it will be cool for our fiber stacking project.’
‘How much did you get of each?’
‘Well, you can only buy a whole number of meters. I got 25 meters in total. And the average core diameter is three microns.’
‘Okay…’ the bachelor student returns to sorting fibers, then he looks up. ‘Why did you get more of the…’ he starts, having figured out the right numbers.
‘The price’, the Phd interrupts him laughing.
The bachelor student laughs too. ‘And that is why you only got one meter of the one-meter of them?’
‘Actually, I’ve been wondering…. Why is everyone in this group giving out numbers in this weird format?
The PhD student looks taken aback, then he shrugs.
‘The Calendar Team started it.’
‘Ah, I understand’
© nqo

15th of December

Published 16th of December. Sign up for the mail box if you want to receive emails with the Calendar 💌

The current and former bachelor students and the current master students were responsible for planning the Christmas party this year. Three former bachelor students are preparing for the pre-party supermarket-trip.

'I got bags, you got the list, the others are picking up the cart...' the first one says.

'Exactly, I think we are ready to go,' the

second answers.

'We also go past the special store, right?' the third asks secretively.

The postdoc who sits in

the same office raises an eyebrow.

'Sure!' the first one says 'but he only takes cash...'

'Oh, I don't have a lot of cash...'

'I also don't.'

'I think it will be 25 euro. I have 10 euro.'

'I also have a 10'er!'

'Me too!'

 'We cannot divide 25 by three. So, of the five euros we get back we will each take one euro each, and the two euros go into party box.'

 'So...' the postdoc turns very slowly in his chair. He taps the fingertips together, looking from one student to the other. 'I have a question. You all pay nine euro. And you put two euro aside. That does not add up to 30 euro... What happened to the last euro?' he looks at them.

The bachelor students all laughs, first in surprise, then of the little riddle.

'That's pretty obvious!' one of them says.


Is it? What happened to the one euro?

© Nqo

16th of December:

Recently a mail went around with a warning that a batch of commercial photodiodes have a bad connection. The two bachelor students are looking at the photodiodes in stock.
‘… the serial number is printed so small!’ one of them says.
‘Where do you even see it? Oh it is very small.’ The other bachelor student holds the photodiode so close to her face that it almost touches her glasses. ‘Is that a three? No, it is a B. No, definitely no threes in this number. Oh look, the last three digits in my serial number is three times as large as the number you got. I mean, as the last three digits.’
‘Weird. I thought they would be in a consecutive order…’ the first bachelor students says. ‘Let me just open this other one. Oh, wow, it is not consecutive at all, but with these three three-digit numbers we have all numbers between 1 and 9.’
‘And they almost sum to 1000!’ the second bachelor student says happily, then she has to modify her statement with a little shrug ‘Ok, not totally, but 1008 is very close…’
‘Let me see…’ the other one says ‘Ha, yes, you are right! But actually, look, the soldering is where it is supposed to be on this one.’
‘On this one too. And this one’
‘Phew, no problem then!’
What are the three-digit numbers?


17th of December:

The two PhD's, a PhD from another group, and the postdoc regularly go to the Gym in the morning.
The PhD students discuss what to do next while the postdoc slowly finishes her last set.
'I KNOW it is leg day, but it is so nice and empty today...' one of them says convincingly.
'Do we really want to skip leg-day?' another asks, not completely disliking the idea.
'I have that problem with my shoulder still, so maybe not too heavy for the shoulders... but there are many other exercises that are not for shoulders and not for legs.'
'Yeah, take care with that. Maybe I'd like to take care with my knee too.'
'Ok, let's make a plan. We go to the leg-machines now, and then we do free weights afterwards. Curls and stuff.'
'I realy have to step up my leg game later, though. I only did 12 kg in that one exercise... And you did 45.'
'But you have to take care with the knee, don't risk it'
'I think I could add... This much' the PhD grabs two weight-pieces from the floor. They add up to a number which is rare in the fitness studio, but fitness studios are full of surprises.
'I think I can add the same weight to my 45, though, then I'm still doing three times as much as you are...' the other PhD student teases.
'I can live with that, though... If you can do four times as much as me I'll buy you a Frikadelle brötchen!'
'Enough. Legs. For. Today' the postdoc gasps. She has finished her final set and leans against the rack.
'Sounds good!' 'cool' 'free weights, then?' the three PhD students says.

How much did the PhD students lift?


18th of December:

This puzzle appears in a very similar form in the amazing book Professor Stewart's Casebook of Mathematical Mysteries. See the introduction for more information about good riddle-books!

'Are you all three going to the city center?' the professor asked with a hint of dissapointment in the voice.
'Yeah' both daugthers said in unison. 'And you can't come, because we will get your Christmas gift.'
'When will we do the match-stick games, then?' he asked.
'When we get home, of course!' the youngest daugther said.
'No, we have to watch the soccer match!' her sister intervened.
'Yeah, I think it will be rather interesting.' their mother said.
'Then after that?' the professor asked. 'Unless there will be overtime and all of that.'
'I don't want to watch soccer.' the youngest daugther said. 'I'll bake pancakes.'
And so it came to be.

The older daugther handed her dad a plate with a stack of four differently sized pancakes.

'Sort them by size, please.' she said. 'No, not with your hands. You have to use the spatula instead.'
'Then I have to flip the entire pile... or at least the pile that is above a certain pancake of interest.' her father said.
'How many flips do you have to use to get it right? Can you do it in three flips?' the younger daugther asked with her mouth full.

Bonus question
'Do I only get four?' the professor asked.
'No, you can have another one. Hopla. Now you have five.'
'What is the smallest number of flips necessary to order an arbitrary pile of five pancakes?

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The pile looked like this

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And this is an allowed move.

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19th of December:

Updated with corrections on the 20th.

'Wait, go back - eh - Can you hold it more still?' the postdoc put his face all the way to his screen.

'Yes, sorry, but I need to get a better grip on you.' the PhD student tried to hold the cell phone more still while taking the lid off the box.

'It feels like Blair Witch Project' The postdoc, who is participating in the unboxing from abroad, laughs 'Oooh, now I see it.'

'Better, right?' the PhD moves the cell phone around to give the postdoc the best possible view on the new suptter-coating-machine-compatible fiber holder.

'Yes, wow, it looks just like we designed it!'

'Yeah, it is pretty cool. Even sorta Christmas-y.' the PhD is pretty satisfied.

The substrate clamps are ordered in a star-like pattern. This idea was build by the mechanical workshop, who found this particular design very appealing. 'Each fiber needs to be clamped with four clamps, and the clamps are super expensive,' they had told the PhD student. 'This design is ideal, because you can clamp any number of fibers in a clamp, and here we use the clamps fully!'

'Great that we will be able to bake five fiber-pieces at the same time!' the postdoc is overly satisfied.

'I was thinking, though,' the PhD student says slowly.

'Hey, what are you doing?? Where am I?' the PhD has put down the postdoc, who sees nothing now.

'To make it easier for the workshop, if we ever need to do it again, we could make one for six fibers with only two more clamps.'

the PhD starts to sketch.

​What does a system with 12 clamps and six fibers look like? Keep in mind that every fiber needs four clamps.

Bonus question

'Show me!' the postdoc says. The PhD student lifts the cell phone and holds it above the drawing. Then, upon seeing it on the screen, he gasps.

'No! Seven fibers! I can make it with 12 clamps and seven fibers!'

​'Oha' the postdoc says, not hiding that he is impressed. 'How exactly?'

What does a solution with seven fibers look like? The length of the fibers are not important.

(Why do they need to coat the outside of the fiber, you might wonder. The fiber team has their reasons.)

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20th of December:

'Thank you all', the former PhD said happily. He looks a bit overwhelmed as he receives hes ceremonial hat from the master student.
'Wow, this is so cool!' it is really cool! He manages to solve the games, he is allowed to put on the hat. They all cheer for him. There is also a cart.
'Oh and Rubo is there!' he says. 'Wow it looks amazing!'
Then he is pulled around the block in the cart. On the first half of the route they have to wait for a bus to pass before taking the streets. The bus driver honks and waves happily. This brings the average speed of the first half of the route to 2 km/h.
Halfway two new cart-pullers take over, and they are FAST, bringing the average pace to 6 km/h.'
'Phew, that was fast,' a very senior person says, looking at his watch. '2 km/h first, then 6 km/h. That makes on average 4 km/h.'
'Huh, no it isn't?' a bachelor student asks.
'Sure it is,' the very senior person says cheerfully, then he looks thoughtful. 'Or is it?'
Who is right.

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21st of December:

'Here is the restock!' the postdoc announced

'Oh, finally!' the PhD said happily and got up from his seat, 'I was nervous that it wouldn't get here before Christmas!'

'We got lucky. Maybe there will also be post tomorrow, but I'm not sure.' the postdoc said.

'It is just so much nicer to have,' the PhD shrugged. 'I had not imagined that we would use one third of them when we changed the MOT.'

'Then we also gave some away', the postdoc recalled. 'I don't know how they always run out before us.' he added thoughtfully

'Yeah, but they actually only took two in the end, they brought some back. I think they found their stock,' the PhD laughed, 'but now they are running low too'

'And then we used two thirds of what remained when we did the horizontal imaging setup...' the postdoc said

'And that is how we ended up with just twelve assorted ones left...' the PhD summarized.

'But now we have a lot!' the postdoc said.

'Yes! Let's go look at the dipole trap setup, I want to see the beam hitting the atoms today!'

How many of the useful things were in the lab initially?

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22nd of December:

'And how are the pins distributed again, and which wires did you connect?', the former postdoc asks. He is remote-assisting the HiWi with a FPGA project.

'Hmm, the diagram is a bit tricky,' the HiWi says slowly.

'There is a ground pin next to a ground pin. And to the right of a yellow wire I connected a green wire.'

'Your wire-color-code is not really standard...' the postdoc laughs.

'Yeah, I know, I brought it home to look at it and got completely silly colors. And I also think I connected them not so cleverly.' the HiWi laughs as well.

'Doesn't matter, as soon as the other cable arrives, you'll replace it.'

'Exactly. Left of a ground pin I have a P1, so singnal pin 1. And left of the blue wire is a yellow one.'


'And right of a yellow I wire I have a blue wire. And finally, signal pin 2 is to the right of a ground pin.'

'I see, this we will figure out!' the postdoc says confidently.

What are the four pins and what color cables are connected to each of them?

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23rd of December

'Yes, absolutely! But everything is well here.'

The doctor in biology is on the phone with her neighbour, who happens to be the postdoc who is also the head of the Calendar Team.

'Oh man - and for how long did you speak Danish to the students? Hahahaha, noo, I think they found it funny. It happens to everyone.'

she moves around on her marvelous balcony while speaking. She is arranging some more pine-twigs along the balcony edge.

'Hold on, I'll just put you on speaker. Do you still hear me?'

'I do!' the postdoc's voice says from the phone 'But I'm just blabbing about myself, what are you up to until Christmas?'

'Noo, you are not blabbing.' the biologist says as she heaves a chain of fairy lights from indoors. 'I'm gonna run some errands and then I go to my mum. But first I'll hang some lights on the side of my balcony, you know, where my lavender and the little bush stands.'

'Oh, you send me a picture when you are done?' the postdoc asks.

'Absolutely. I'll hide the battery-thingy in the pink bucket, you know, and... hang on.'

'I'm here,' the postdoc says.

'So!' the biologist says, 'phew, okay I'm back.'

'Does it look good?'

'YES! The wire goes as six straight lines starting from the bucket, and it is tangled on all my plants.' the biologist says with satisfaction.

'That sounds good,' the postdoc says, though she shivers at the other end of the line by the thought of crossing wires.

Below you find a sketch of the part of the balcony where the biologist is hanging the fairy lights. The red crosses are the plants which have to be touched by the wire. The wire starts in the bucket, which is marked by a circle. Each plant is only touched once by the wire.

(You might also notice that the neighbour of the biologist has not been so good at taking care of her plants since the tomato plant stopped giving tomatoes...)

How does the wire go?

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24th of December:

This question contains bonus questions! However, a correct answer is a correct answer, whether it is for the 'normal' question or a bonus question. The Calendar Team is very happy if you email any solution to the Calendar email.

'What are you doing?' the professor pulls a chair out. He has a box of matches in his hand, hoping that he can crack a few games.
'Mom came up with this new game.' the older daugther says.
'It is really difficult,' the younger one says.
'Will be trending on TikTok in no time for sure,' the older one says.
The daugthers are moving boxes over the table. They are cubic and have a large Christmas tree on one side.
'Eh, okay... I saw something online, though, it is a dog of matches.'
'There are almost no match-things on TikTok anymore' the younger daugther says with a shrug. 'Oh, how about rolling it like this.' she says excitedly to her sister, showing her a move with a box.
'Oh, yeah, that is smart!' her sister says. Then she seem to think for a bit. 'Do you also want to play, dad?'
'Eh, sure! Though I actually thought... There is also this fish of matches. But okay, what is with the boxes?' he pushes away the box of matches.
'Did anyone say fish of matches?' the door opens
'Hi mom,' the daugthers say in unison. 'Yeah, dad wants to play with the matches again.' the older daugther says.
'No, I want to do the boxes too,' the professor says hurridly, then changes his mind. 'There is also a dog of matches,' he beams at his wife, who sits down too.
'Oha,' she says, but honestly, she also seems more interested in the boxes. 'Show them to me later. First, hand me those boxes'
'But mom, we almost have it.' the older daugther protests as they hand over the cubes.
'Sure, but dad can help you figure it out. Look, you make this plus of the cubes. And then you rearrange them to this shape.'
she moves the boxes around, and turn one of them such that the Christmas tree is lying down.
'Now the question is, where is the middle box in the new figure?'
'That is easy,' the professor says puzzled, pointing. 'It is that one.'
'Yeah, when I just move them like this it is this one.' his wife says patiently. 'However. You cannot move them like this, you can only tip them over one edge. Like this.' she demonstrates by rotating one cube. Now the Christmas tree is on the side of the cube.
'Oha, that is of course different...'
'Yes, but I'm sure you will figure it out,' she says with a twinker in the eye, then she adds, 'But maybe first show me the stick fish.'
'And the dog!' the younger daugther cheeps, who seems more interested now that the boxes have been moved out of her hands.
Maybe there is still room for playing with match sticks, the professor thinks.

Which box was the middle one?

Bonus question:
'So the fish...'
'The dog first' the younger daughter interrupts.
The professor starts putting the matches.
'I think I know it!' the older daugther announces. 'The dog must look the oher way.'
'Hey!' her dad says. 'Do you know the solution? Did you see this online?'
'No, I haven't seen it before, but it seemed logical.'
'You can move two sticks.' the professor says.
'I'd move... Those two' the younger daugther says. 'What do you think'
'Sounds like a good move.'
'Too easy'

Bonus bonus question:
'Okay, this is the fish... And there seems to be a theme here.' the professor laughs.
'So we turn it around?' the younger daugther asks as she puts a raisin on the fish to indicate an eye.
'Indeed,' the professor says. They all laugh. The younger daugther puts more raisins as air bubbles.
'With how many sticks?'
The professor thinks for a second 'Try just one.'
A second second of silence follows. Then: 'Huh!? Nooo' 'What?' 'That cannot be.' the daugthers and their mother say loudly together.
'No, sorry, I'm teasing you,' the professor laughs, 'You need to move three sticks.'
'That's so lame.' the older daugther sighs. 'it is too easy now.'
'That's not fair, dad' the younger daugther complains as she moves the sticks and turns the fish. She has to move the raisins to make it right.
'One would be a true challenge!' the wife of the professor says and leans back in her chair.

Bonus bonus bonus and bonus x 4 question.
'Okay, I have one which is truely challenging,' the professor says, now more serious. 'Then we do the cubes afterwards, okay?'
'Show it!' the older daugther says excitedly.
'So now it is an equation. and we want it to be approximateively correct. You can move one stick.'
'And can we change the equality sign?'
'Oh, difficult!'
Half a minute of quiet follows.
'I'm almost there', the older daugther finally breaks the silence. 'If I move two sticks I get it exact.'
'What?' the professor looks carefully at the equation. 'I didn't even see that one! It wasn't what I thought of, but it is really good.'
'Was this what you were looking for,' the wife asks.
'How? Yes, yes it is! Damn, you crack even the hardest ones.'
'I know,' his wife laughs and gets up. 'Now I'll get something to drink, and then I want to see you three solve the box problem.'

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The stick-riddles follow:

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Wird geladen