###### Christmas lab calendar 2020 - SOLUTIONS

December 01, 2020###### Publications in Phys. Rev. A and Phys. Rev. Research!

December 09, 2020Every day until the 24th this post will be updated with a new lab-themed challenge!

If you have solved a challenge, you can email your solution to Nina.

Answers are accepted until six the day after they have been asked – and weekend-answers (Friday, Saturday, Sunday) will be accepted until six on Monday. To be clear, Nina is happy to receive answers to the question from the 1st of December until 18:00 on the 2nd of December.

The solutions will be posted here: https://nqo.iap.uni-bonn.de/wordpress/christmas-lab-calendar-2020-solutions/

Between Christmas and New Years we will find the Calendar Winner by drawing lots between all the correct answers ?

The riddles are adapted from Daniel Smith: *How to Think Like Sherlock- Improve Your Powers of Observation, Memory and Deduction*, Ian Stewart: *Professor Stewart’s Cabinet of Mathematical Curiosities*, Carl-Otto Johansen and Arne Hansen: *Hovedbryderen – Politikens håndbog i hovebrud 3*, and ing.dk

**1st of December:**

The PhD student is connecting equipment in the lab.

- The aircon (1) must be connected to a controller (A).
- Some instrument on table (2) must be connected to the computer (B )
- The lasers on table (3) must be connected to the UPS (C)

Is the PhD student right when she claims that she can make the three connections without crossing the cables?

How can she do this?

**2nd of December:**

The postdoc encounters three boxes where the labels have been messed up by someone……..

The labels say

- Imperial Screws
- Metric Screws
- Imperial screws and metric screws (mix screw box)

Not a single label is matching the content of the box it labels.

What is the minimal number of screws the postdoc needs to look at in order to relabel the boxes correctly? And from which box(es) should he take this low number?

And the postdoc KNOWS that EVERY BOX HAS A WRONG LABEL.

ALL LABELS ARE UNTRUE! THE LABELS ARE A LIE!

(For my friends in chemistry and beyond, the boxes could also be labeled ‘Apples’, ‘Bananas’, and ‘Apples and Bananas mixed’. Except that it can be a lab-sin to make a mix-box with imperial and metric screws.)

**3rd of December:**

One of the master students have to give a Friday Physics talk tomorrow (true story!), and he initially made too many slides and had to delete a lot again. The other master student asks how many slides are left.

“Well, this morning I had more than 20 slides. Now I’m down to having so many slides that if you would pick two distinct slides at random and delete them, the probability that both of them show some of my results is exactly one-half.“

“I see,” the other master student answers.

How many slides do the master student have? (nothing is actually deleted by the other master student!) And how many of his slides contain his results?

**Bonus question:** The statement (pick two distinct slides and probability of results on both of them is ½) also held when the master student had more than 20 slides. What is then the first solution to the problem?

**4th of December:**

- The first has the numbers 3, 4, and 8
- The second has the numbers 6, 2, and 7
- The third features 1, 5, and 9.

**5 ^{th} of December:**

Julia is a teacher at a Danish high school, and not all of her students are excellent (True story! This is in fact one of the reasons why the answer from the 3^{rd} is delayed!).

One of her students has solved a question in a rater interesting way. He has rewritten a product of fractions like this:

(1/4)*(8/5) = 18/45.

*In the email, I had a typo in the equation above! Here it is correct.*

Julia knows that he has done this weird addition instead of actually doing the multiplication, but he actually ends up with the correct result.

For what other fraction pairs (a/b * c/d) where a, b, c, d are single digit integers could the student get the right result with his method?

Bonus question: What if a, b, c, d can take double digits?

**6 ^{th} of December**

The PhD wants to connect six components on a print board such that

- Input 1 is connected to components A, B, and C
- Input 2 is connected to components A, B, and C
- Input 3 is connected to components A, B, and C

She has this weird aversion against crossed cables, so she wants to do it without crossing the cables.

How can this be done?

**7th of December**

- The postdoc sits next to the ytterbium PhD, but not next to the master student.

- The master student sits next to the supervisor but not next to the rubidium PhD

- The rubidium PhD sits next to the ytterbium PhD but not the supervisor

**8th of December**

The supervisor has a calendar which used to sit on his desk (now it is probably packed into a box).

The calendar consists of four dice which can be turned such that they show the current date (day and month).

Sometimes during boring meetings, a certain PhD student dwells on the of the construction of such a calendar.

Considering only the day-cubes, what numbers must be on the two cubes such that they can represent any date from the 1st (01) to the 31st (31)?

**9th of December**

**December 10th**

One of the two ytterbium postdocs is in quarantine together with his wife. They have come up with a fun game. She draws a figure, and he makes a laser pointer beam path identical to the figure.

The postdoc does not have any beam splitters, glass plates, or semitransparent mirrors in quarantine. He can only use mirrors, but the mirrors can have more than one reflective surface.

Assuming the laser pointer takes up no space, is it possible to recreate this figure?

For my friends in chemistry and beyond (and also for the physicists in case the above question was too weirdly formulated) I will reformulate the question: Can you draw this figure without lifting the pen and without going along the same line twice.

**Bonus question!**

The PhD student who dislikes crossed cables has heard of this fun game, and she now wants to create this figure with a cable – without the cable crossing itself!

Happy puzzling 🤶

**11th of December**

The postdoc has picked up an order from the mail room. Due to lead time on some of the purchased product, only part of the order arrives. The master student – who has his birthday today, congratulations! ? – asks what the postdoc has picked up.

“We ordered amplifiers, adapters and the jumpers we were out of. Today received 100 items, and curiously the total price of what arrived today is also £ 100!”

“Funny,” says the master student, “what do they cost again?”

The postdoc answers that

- The amplifiers are £ 10 each
- The price for one adapter and two jumpers is £ 4
- One adapter is £ 2 more than 2 jumpers

The master student thinks for a second, then he says:

“I see. I think I know what arrived.”

How many amplifiers, adapters and jumpers arrived?

We are not interested in pairs of jumpers, but in how many individual jumpers have arrived 🙂

**12th of December**

**13th of December**

It is Sunday and the supervisor is baking a cake for the group 🍰

After he has paid the salary of the little baking-helpers, the cake looks like this:

(But less 2-dimensional and more delicious, the group members look forward to it!)

Two of the eight group members are in Germany, so the cake will have to be cut into six pieces. What is the lowest number of straight cuts necessary to cut this cake into six pieces?

Happy cake-cutting! ?

**14th of December**

- The first student said that picture 1 showed Heisenberg and picture 2 showed Planck
- The second student said that picture 3 showed Planck and picture 5 showed Heisenberg
- The third student said that picture 2 showed Bohr and picture 3 showed Dirac
- The fourth student said that picture 4 showed Pauli and picture 1 showed Dirac
- The fifth student said that picture 2 showed Bohr and picture 4 showed Pauli

**15th of December**

The postdoc and the PhD are cleaning some tools with some organic solvent, but they acidentally break the beaker when dropping the tools into the solvent. They make four small holes in the bottom of the beaker.

- If the beaker had only hole 1, it would empty in 3 minutes,

- If the beaker had only hole 2, it would empty in 6 minutes,

- If the beaker had only hole 3, it would empty in 10 minutes,

- and if the beaker had only hole 4, which is a tiny crack, it would take 15 minutes before the beaker would be empty.

However, the beaker has all four holes.

**16th of December**

The master student is writing come experiment code and discussing it with the other master student (the discussion is online for corona-safety 💬). The code produces a file with a number of dictionaries which all contain the same number of elements.

- then he removed 10 dictionaries and and distributed their elements in the remaining dictionaries, such that each remaining dictionary got one additional element.
- during this discussion, he has removed further 15 dictionaries and he has distributed their elements in the remaining dictionaries.
- After the superfluous dictionaries have been removed, the remaining dictionaries have 3 elements more than before the dictionaries were deleted.

How many dictionaries did the student have before he got rid of the 25 superfluous dictionaries? And how many elements did each dictionary have? What is the number of dictionaries and elements after the code revision?

**17th of December**

After learning today that a lot of people are *actually* looking at the webpage entries I would like to apologize for not being so consistent of updating this page as soon as I send out the email (usually I send it at 9 except for in the weekends) – Sorry, I wasn’t aware! And yes, the questions come as emails too!

In the email of today I also informed that I will find the Calendar Winner at some point between Christmas and New Years. The winner will be picked by a draw between the correct, submitted answers. So if you have not yet participated, you can still enter one or more answers and enter the lottery 🍀

Answers should be sent to me on email.

If you would like to receive the calendar emails, you should also just drop me an email 📧

Cheers,

Nina

And now for the question!

We are looking for a path that minimizes the length of the connection. The solution on the screen is not optimal. It has a total pathlength of 2*sqrt(2) PCB length units. Show her that it can be done better!

**18th of December**

Today his calendar has six entries from three different categories:

- Friday physics with group (Talk)

- Meeting with rubidium team and collaborators (Supervision)

- Faculty meeting (Administration)

- Meeting with student (Supervision)

- Listen to seminar talk (Talk)

- Final before-Christmas administrative meeting (Administration)

the supervisor notices a pattern. He has

- Three other meetings between the two talk-entries

- Two other meetings between the two administration-entries

- One other meeting between the two supervision-entries

**19th of December – prelude**

**19th of December**

**20th of December**

Today’s question(s) goes out to three guys who are always ready to help a friend in need. Even if it is a matter of revealing deeply secret and forgotten passwords! Thank you 🤶

Therefore, we have three questions, and each correct answer counts as an additional lottery ticket in the final draw for Calendar Winner 😊 (send them to me by emaiiiiiil)

The company where Christoph works sends out greeting cards to customers, and Christoph wants to sign seven of the cards. It turns out that the person who packed exactly those seven cards was not paying attention, and for each card put an address sticker picked at random between the seven addresses.

- What is the probability that Christoph finds exactly six of the cards in envelopes with the correct address?

Asaf is one of the persons who ought to receive a card signed by Christoph. While Christoph signs the cards, it is night in Mexico, and Asaf is wondering about the moon.

- What is actually the shape of the crescent moon – It is not a large circle with a smaller circle inside as I have drawn it.

We are assuming that the moon is a perfect sphere, and that the light from the sun can be described as parallel rays.

Christoph also hopes that young Christoph gets to see one of the cards. While the cards are being signed, young Christoph and hispostdoc are screwing some things to an optical table. Christoph points out that screws with circular heads are nice since the heads always have the same width independent of the angle.

The postdoc answers ‘Ja, sure, that is nice, but I can also think of at least one other curve with this property’.

- What other (classes of) curves have this property?

PS. if you also want a calendar appearance, I can be bribed with chocolate and such.

I should have said this earlier, actually!

**21st of December**

Somehow it is always windy in Denmark, especially when the PhD student is biking to the university.

On the way to the university she has the wind against her, and can only make an average speed to the university of 12 km/h.

On her way back the wind is better, and while biking she makes has an average speed of 18 km/h. However, she has to wait in seven out of seven (!) traffic lights, and loses on average 55 seconds in each traffic light.

She lives six kilometers from the university.

Is she faster when going to or from the university?

**Bonus question:** What is the speed of the top point and the bottom point of the bike wheel when the PhD rides with 18 km/h?

**22nd of December**

You know that vacation feeling of not knowing what day it is?

The supervisor has just left the home office and asks

‘When will they show that movie we always watch on Christmas?’

His wife, who keeps better track of time, looks up, and says

‘The day after tomorrow, they show it quite late this year.’

The supervisor thinks for a bit, and asks

‘What day is it actually today?’

The older daughter sighs and shrugs ‘Friday’.

The younger one chirps ‘No, Saturday’

‘Uhm, what day is it tomorrow?’, says the supervisor, who wants to avoid some argument.

‘Monday’, says the younger one.

‘Tuesday’, the older one suggests.

‘You have me a bit confused, what day was it yesterday’, asks the supervisor

‘Wednesday’, says the older one.

‘Thursday’, the younger one corrects.

‘You have both given two wrong answers and one correct one,’ the wife laughs.

‘We can anyway probably just stream the movie if you want to watch it right away’.

- What day is it today?
- What day is the movie shown on flow-TV?

**Bonus question:** What movie are they talking of?

**23rd of December**

Merry Christmas! 🎄

I hope you are all safe and happy.

This is the last calendar entry for now, and again I will just say THANK YOU for participating in this calendar, it has been a great pleasure to prepare, and I hope you had as much fun as I did! 😉 You have really exceeded my wildest expectations.

As announced already, I will draw a winner of the calendar from the correct answers around New Years. If you have not submitted answers to the questions from the last few days, you can still make it, just drop me an email 🤶

Also, today’s challenge is surprisingly well suited for sharing with family members!

**24th of December**

Between Christmas and New Year some group members and some friends meet (online) for a Christmas greeting.

The postdoc sets up the meeting, and looking at the others, he notices that:

The meeting is scheduled for 14:30, but some are a bit early and some are a bit late. No-one enters the meeting at the same time. They join the meeting from different locations, and they are each eating something different. In the meeting, they discuss how they did or did not celebrate Christmas, and they each talk about a Christmas gift they received (and discuss gift-free Christmas).

After noticing this, the postdoc texts the always problem-solving master student, who will only join later:

‘Can you tell me who joined when, who eats what, who got what for Christmas, where they join from and what colors they are wearing?’

The master student writes back:

‘What?? 😅’

‘I write you some hints 👍’

‘Seriously, why are we always playing these games??? 😅’

‘Because it is fun! You get these hints and these categories 😊’

The hints are:

- The person with the red T-shirt joins from the kitchen
- The PhD we know already got books for Christmas (and already read the first two!)
- The person who is eating an orange considers the corona vaccination for a family member the greatest gift
- The student from applied math joins from the office
- The arrival time difference between the person who joins from the university and the person with the blue T-shirt is one minute
- The person who is happy about gift-free Christmas arrives just on time (14:30)
- The biology PhD wears a green T-shirt
- The person who is eating Studentenfutter wears a blue T-shirt
- The arrival time difference between the person with the gray T-shirt and the person who received kitchen equipment is one minute
- The person with the black T-shirt got a cool sweater for Christmas
- The arrival time difference between the chemistry PhD and the person eating Rye bread is one minute
- The researcher from the engineering department is eating marzipan
- The person who eats an orange arrives one minute earlier than the person, who eats Christmas cookies
- The chemistry PhD is the first to join the meeting
- The arrival time difference between the person who wears a gray T-shirt and the person joining from the bedroom is one minute.

The participants are, apart from the postdoc and the master student:

A student of applied math, a biology PhD, a chemist, one of the PhD’s we know from earlier calendar entries, and a researcher from the engineering department

They arrive between 14:28 and 14:32.

They eat Marzipan, an orange, Christmas cookies, rye bread and Studentenfutter, and joins from office, kitchen, bedroom, university and living room.

Someone got kitchen equipment, someone else got books, someone got a home-made sweater. One appreciates not to fuss about gifts, and one considers the corona vaccination for a family member the greatest gift (after hearing this, the person who started out telling about the super nice kitchen stuff feels a bit superficial)

The T-shirt colors are green, black, blue, gray, and red.

The master student takes longer than usual, but then texts back ‘I see! 👍 Looking forward to joining and checking my result’

Who joined when, who eats what, who got what for Christmas, who joins from where, and what colors are they each wearing?

(I attach a table that I recommend using, but you can also go full logic-puzzle and try without :O )