Puzzle Booklet 2021 by Ideaal! (Abacus)

S Association magazine of W.S.G. Abacus

Campus Photo Hunt Codebreaker Sudoku Geoguesser Sudoku Puzzle Booklet 2021

INDEX 4 5 5 6 15 16 17 18 19 19 20

New Puzzles Hashiwokekero TOOT Numbers on the Table Campus Photo Hunt Barcode Puzzle Battleship Bermuda Triangle Codebreaker Sudoku Keep the Chairman Healthy Skyscrapers Chess Puzzles AMW Puzzle Tour Get the Code! Word Search Penrose Tiling Slitherlink US vs UK Anagram Quotefall Logiquiz Killer Sudoku Logos

29 30 32 33 34 36 41 2

Nostalgic Puzzles Eastereggs Cryptic Crossmath Roman Crossword Trains Big Logiquiz Geoguesser Sudoku Puzzle Sequence

21 22 23 24 24 25 25 27 28

Editorial Dear reader, After a few years and many requests, the Ideaal! is finally bringing to you a puzzle booklet! As you might know, usually the Ideaal! is printed and handed out to all who are interested. This also means that usually you can solve the puzzles included with pen and paper as was intended by their creators. Due to this year’s circumstances, that has not been possible for the past few editions. This is the reason why we decided to physically bring the puzzles to you outside of this year’s last edition in the form of this puzzle booklet. For old times’ sake we even included puzzles from old editions and the ones utilised during the Active Members Weekend this year!

We are especially thankful to you, the reader, for supporting this project by signing up for this booklet. We really hope you will enjoy all of the puzzles. Of course, you should also make sure to read the newest edition of the Ideaal!, Sunny Side Up 2021! For now, we wish you a pleasant summer and lots of fun solving the puzzles in this booklet. See you next year! The Ideaal!

We are very thankful to everyone who helped out making this puzzle booklet possible by either providing a puzzle or proofreading this booklet and checking the solutions to all of the puzzles you can find in here.

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 Timon Veurink

Guest writers: Jorn de Jong (TOOT, US vs UK), Matthew Maat (Numbers on the Table, Bermuda Triangle, Keep the Chairman Healthy), Anouk Beursgens (Campus Photo Hunt, Anagram), Thomas Kanger (Chess Puzzles), Daan Velthuis (Get the Code!), Luuk van der Werf (Word Search), Daan Pluister (Penrose Tiling Slitherlink, Geoguesser Sudoku, Puzzle Sequence), Martijn ter Steege (Quotefall), Marjolein Bolten (Logiquiz), Linda ten Klooster (Killer Sudoku), Sanne Oude Veldhuis (Logos), Stefan Klootwijk (Eastereggs, Cryptic Crossmath, Roman Crossword, Trains, Big Logiquiz).

Hashiwokekero Text: Jorg Gortemaker Hashiwokekero, “Build bridges”, is a Japanese puzzle where it is the objective to connect the dots, “islands”, with straight lines, “bridges”. There are a few rules you’ll need to follow to complete this puzzle:

1) Every dot has to have the same amount of bridges connected to it as is shown on the dot. 2) Bridges can only go vertical or horizontal, not diagonal. 3) Two dots can at most be connected by two lines.

4) At the end all islands should be reachable, i.e. there exists a path from any dot to any other dot.

TOOT Text: Jorn de Jong If you used something, don’t even look at it

again, ignore it, and have fun!

Numbers on the Table Text: Matthew Maat On a table, there are some seemingly random numbers, which share a nice mathematical property. Can you find the next number in the sequence? 142857, 0588235294117647, 052631578947368421, 0434782608695652173913, … Hint: you might want to use a computer for some calculations.

Campus Photo Hunt Text: Anouk Beursgens The campus is a beautiful place to make a walk. You can find the weirdest pieces of art, the most idyllic nature and the most creative names and logos of student houses. Can you

Category: Buildings

find out where all these photos are taken? If you know the campus well, you can make it even more challenging by doing it off the top of your head.

Try to find out the sum of number in the photogenerating squares, per category. Good luck!

Category: Nature

Category: Objects

Category: Signs

Category: Student Houses

Barcode Puzzle Text: Timon Veurink Some packages were lost by the postal service, but they seem to be very important. Luckily you can see the barcodes and decide that they must contain a clue to whom they belong to. Can you figure it out?

Battleship Text: Daan Pluister Find the ships placed by the active members during the train game of the active members weekend. The clues indicate how many ship parts are in

the respective row/column. One ship may not touch any other ship, also not diagonally. Every grid contains all the ships available.

Bermuda Triangle Text: Matthew Maat Oh no! You fell asleep behind the steer of your boat and now you are lost somewhere in the Bermuda Triangle! In this infamous area, your compass is spinning in circles and the sun is always behind the clouds, and there is no way to find directions or call for help while you are inside the triangle. There is no wind or current in the ocean, so you can only move by using your engine. Also, you remember the Bermuda Triangle has the shape of an isosceles right triangle,

of which the length of the longest side is 100 km. When you look at your tank, you see you have enough fuel for exactly 100 km. You’ll know when you are outside the triangle because then your radio will work again and you can call for help. (assume you are able to measure distance you went, angles of turns you make etc.) Find a path that you can take to make sure you leave the Bermuda Triangle at some point in your journey.

Note: For example, you cannot just go in a straight line, because you could be exactly in the corner of the triangle, so you need to find a smarter strategy to navigate your boat to make sure that at some point you get outside the triangle, independent of where you start or which direction you face at the start.

Codebreaker Sudoku Text: Tim Hut Fill in the shapes in the 9 by 9 grid using normal sudoku rules. Similarly and independently also fill in the shapes Together they will form a symbol that will help you decode the following word:

Keep the Chairman Healthy Text: Matthew Maat We have a lot of bowls, a positive integer k and k colours of M&M’s. We fill some bowls with M&M’s, but with the following rules: • We cannot put multiple M&M’s of the same colour in a bowl, and we must use all colours. • For each pair of colours A and B: - There exists a colour C (C could also be colour A or colour B) with the property that,

if a bowl contains an M&M of colour A or colour B (or both), then it must contain an M&M of colour C. - There is some bowl which has an M&M of colour A but not of colour B or the other way around (so we divide different colours in a different way). • Out of courtesy, we must give the bowl with the most

M&M’s to the chairman of Abacus. However, we want to give a specific amount of M&M’s to the chairman, so our goal is to make a division of M&M’s over bowls (you can use as many bowls as you like) for the following cases (increasing difficulty): 1. k=5 and 4 M&M’s for the chairman 2. k=9 and 6 M&M’s for the chairman 3. k=11 and 7 M&M’s for the chairman

Skyscrapers Text: Lavinia Lanting

Chess Puzzles Text: Thomas Kanger Easy

Medium

Hard

AMW Puzzle Tour Get the code! Text: Daan Velthuis Oh no! The board was not used to come to the Abacus room anymore and they all forgot their key and the code to get to the spare key! Can you help them to retrieve the code such that the board can

once again run the Abacus room? The code is given by the coloured squares. Rules: Fill a digit (1-9) in each white square, such that the sum of each horizontal seg-

ment is given by the clue on the left and the sum of each vertical segment is given by the clue on the top. Some clues are missing however. No digit may be repeated in each segment.

Word search Text: Luuk van der Werf Find all the words, and the first of the remaining letters will give you a hidden message. Who are we? (6) What are you too much when you suffer from ADHD? (6) Who did organise this weekend, among others? (5)

How do you get on Texel? (4) Where should you not fall in? (8) What keeps you alive during the weekend? (6) Big chance you were or are in one of these (10) Where are we? (8) Student’s favourite sport? (10)

Your favourite beverage (7) Your favourite late-night snack (9) Your favourite high school course (11) Which colour is very different from blue? (4) Your favourite Sunday activity (8) Where would we be? (5) Pluister’s favourite vehicle (5)

Penrose Tiling Slitherlink Text: Daan Pluister Fill in some of the dotted line segments to form a meandering path that forms a single loop. The path does

not cross itself, branch, or touch itself at corners. The numbers indicate how many line segments surround

each cell. Empty cells may be surrounded by any number of line segments.

US vs UK Text: Jorn de Jong The candidate secretary Thomas is still using American spelling instead of British spelling. Can you help him find all the British

versions of the words below and answer the question? Of course, ABBA is the same in both languages.

Good luck!

vacuum cleaner

shrimp truck ABBA French fries

buck yard +-630$ everyplace

inventory vacation traffic circle stock

Anagram Text: Anouk Beursgens Instead of going to Texel, of course the most important place of the Netherlands, we will

travel through Europe on paper. And what would a city be without its main tourist attrac-

tion… How many days will our trip take?

Quotefall Text: Martijn ter Steege The best weekend of the year is here, but how nice is it?

Logiquiz Text: Marjolein Bolten During the yearly Christmas dinner all the candidate board members were of course present. But they were all missing something on

the table. To find out what, you also have to find out how they are dressed and what they ordered during the dinner.

Good luck!

Hints: 1. The candidate board member who is missing their plate, didn’t order the steak or quark dessert. 2. Margriet is wearing a tie, and Ruben is missing a napkin. 3. Eline didn’t order the bruschetta or eggplant rolls. 4. Niels didn’t wear a hat, he ordered the quark dessert. 5. The one wearing a dress, orders the eggplant rolls. 6. Ruben is wearing heels, and Thomas is missing a fork. 7. The one missing a spoon, ordered cod filet.

Killer Sudoku Text: Linda ten Klooster The secretary of the board accidentally removed all numbers in his sudoku. Luckily, being a mathematician as he is, he did remember which numbers should sum to a certain amount.

Fill in this killer sudoku completely. The rules are the same as with a normal sudoku except that the sum of the numbers within the dotted-lined figures need to equal the number in its corner.

Good luck!

Logos Text: Sanne Oude Veldhuis The first letters of these logos will form a nice workout exercise.

Nostalgic Puzzles Eastereggs Text: Stefan Klootwijk The goal of this puzzle is to find a four-digit integer code C contained in {1000, 1001, … ,4000}. The three images below, each contain three hidden texts: ‘this puzzle also contains some Easter eggs’, a clue for finding the answer C, and a random quote. If you correctly combine the three clues for finding the answer, then there are still 9

possible codes left. These nine possible codes are placed by a codebreaker on a Mastermind board. Instead of placing the key pegs as usual, the codemaker reveals that (obviously) one of the rows is correct and that |B – W| = 1, where B is the number of black pegs (s)he would need in total for all nine rows and W is the number of white pegs needed

Can you find C?

Cryptic Crossmath Text: Stefan Klootwijk Solve the clues and rearrange the letters in the lightly coloured squares to obtain an appropriate phrase.

For those of you who have no experience whatsoever with cryptic crosswords, the following document provides a nice explanation:

http://playdash.org/ resources/CrypticClueReference.pdf

Across 1. Unfinished French river in the Greek alphabet. (3) 5. One slip changes to an arbitrarily small quantity. (7) 8. Mathematical operator of a series without limit. (10) 9. This convex quadrilateral has no weight after having the same direction. (13) 11. Dislocated hip or golden ratio? (3) 12. An endless Venn diagram in extra time is happening. (5) 13. Adds quantities of money. (4) 14. Even aspect is a collection of elements. (3) 15. Rates that are the inverses of wavelengths. (11) 17. Crazy rider name equals 1 when dividing 51 by 5. (9) 21. Often omitted mathematical symbol used in Morse code. (3) 22. This curve is an endless inverted U. (3) 23. Geometric regions of which number 51 is highly classified. (5) 24. Frobenius is an example of those which are typical. (5) 25. Lines that can be found in selected gestures. (5) 26. A collection of organized things is sincerely yours subject to twelve points. (6) Down 1. Circular straight stick framing the United Nations. (5) 2. Strange property of half the integers. (3) 3. Opposite in poetry. (7) 4. Solid figures with six faces formed by a line of latitude followed by rigid tube inside editors. (15) 5. Search the ukulele mentally for a small part of the whole. (7) 6. Escorts form parts of a circle. (7) 7. Angular velocity is denoted by zero million. (5) 9. Sharpen the Italian river in tea. (5) 10. A crazy mind eraser yields leftovers. (10) 11. Inform you recent, basic principle! (9) 16. Do enough for odd shafts in softy. (7) 18. Names mixed up in averages. (5) 19. 500 equals 16 minutes and 40 seconds on circular plates. (5) 20. Travel over a series of mountains. (5)

Roman Crossword Text: Stefan Klootwijk Each entry of this crossword puzzle is a Roman number. The seven clues are sufficient to fill the grid in a unique way. After having filled all 34 positions of the grid,

you can read a very appropriate number for this issue (the Lustrum edition) of the Ideaal! along one of the rows, columns or diagonals. This number is the final solution.

Clues: A is a square D is a triangular number E is a cube F is a prime G>H A+F=J+M E+I+M=C+C+C+L

Trains Text: Stefan Klootwijk The following puzzle consists of two parts. The first part requires you to think outside the box in order to find the solution. For the second part you are advised to use the internet in order to be able to combine everything and obtain the correct answer (although railway enthusiasts might have a slight advantage here). Three trains pulled by steam locomotives are all heading to a station of which you can see the (schematic) track plan in the picture. The station has two water cranes for refilling the water tanks of the steam locomotives; one is located on the left side between platforms 1 and 2, the other is located on the right side between platforms 2 and 3. In the schematic track

plan they are denoted by a black dot. The coloured squares in the background are placed either on the tracks or directly next to them for distraction purposes. You obtain the following information from the time table. The first train is running on the main line from left to right, and is scheduled to arrive at the station at 15:16 on platform 3 and to depart at 15:50. The second train comes from the main line on the right side and is scheduled to arrive at 15:32 on platform 1; its departure towards the branch line on the left side is scheduled at 15:46. Finally, the third train comes from the branch line on the left side and is scheduled to arrive at 15:33 on platform 2; its departure towards the main line on the left side is

scheduled at 15:40. Note that this implies that the third train needs to change direction at the station. However, at the moment that it arrives, it is impossible to move its locomotive around to the other side since all tracks are occupied. Yet, all trains arrive and depart on time with a steam locomotive running in front, and there are no other steam locomotives being used. How is this possible? (Note: theoretically there are multiple solutions possible, but only one of them will be logical in the real world; use that solution for the second part). Once you have found the correct solution, you can use the distractions to determine the name/location of this station by collecting and rearranging some hidden clues from the right paths of the locomotives.

Big Logiquiz Text: Stefan Klootwijk Last summer, three friends travelled by train from the Netherlands (NL) via Germany (D) and Denmark (DK) to Sweden (S), and back. During this journey they made six border-crossing train trips. Unfortunately, the information concerning these trips has been scrambled. Can you find the correct information for each trip? Note: the departure and arrival times are given according to the schedule, i.e., they are not always the real departure and arrival times. Clues: • The delay of the train with the broken airco was 5 times as high as the delay of the train with a scheduled travel time of 3:16. • The train from the Netherlands to Germany had broken down several times in the weeks prior the trip; due to this risk, the three friends took an earlier train.

• The train with train number 35 took the three friends from Germany to Denmark; on their way back they crossed this border in a train which number is divisible by 5. • The trains with train numbers that are divisible by exactly three different prime numbers arrived with at most 5 minutes delay. • The trains to and from the Netherlands did have at most 1 minute delay; the trip leaving the Netherlands was shorter than the trip entering the Netherlands. • The train number corresponding to this trip that was scheduled to take 4:34 is divisible by 79; the two shortest trips were taken in trains with numbers divisible by 11. • One of the possible routes between Denmark and Germany contains a ferry link, where the train enters a ferry; the guy that inadvertently pulled the emergency brake when

the train was about to enter that ferry, caused an hour extra delay. • Close to the border between Denmark and Germany a train broke down, and it took almost 30 minutes to fix it; luckily, on the remainder of its journey the delay was reduced to only 5 minutes. • The three longest trips turned out to be the most delayed ones, whereas the train with number 20361 had only 1 minute delay. • The trip in the crammed train across the Øresund Bridge from Sweden to Denmark luckily only took 20 minutes.

Geoguesser Sudoku Text: Daan Pluister

1 36

2 2

2 37

4 4

5 38

6 7

8 8

8 9

Puzzle Sequence Text: Daan Pluister This is a series of puzzles where the first fills in clues for the second and et cetera. Mark every square in the first grid with the area of its containing region. Colour the second grid so that adjacent regions are never the same colour.

The gray squares in the third grid need to be lid up by placing light bulbs. A light illuminates its own square and all the squares in the same row or column unless blocked by black squares. Lights may not illuminate each other. Each numbered square must be

orthogonally adjacent to exactly the given number of lights. The last grid needs to be filled with a train track following one line from one light bulb to the other light bulb. A track may not cross or loop. The clues on the side indicate the number of track pieces.

SOLUTIONS 43 43 44 44 45 46 46 47 48 49

New Puzzles Hashiwokekero Campus Photo Hunt Numbers on the Table Barcode Puzzle Battleship Bermuda Triangle Chess Puzzles Codebreaker Sudoku Keep the Chairman Healthy Skyscrapers AMW Puzzle Tour US vs UK Anagram Quotefall Logos Logiquiz Killer Sudoku Get the Code! Word Search Penrose Tiling Slitherlink

52 53 54 54 55 56 56 42

Nostalgic Puzzles Cryptic Crossmath Eastereggs Roman Crossword Big Logiquiz Trains Geoguesser Sudoku Puzzle Sequence

47 47 49 49 49 50 50 51 52

Solution: Hashiwokekero Text: Jorg Gortemaker

Solution: Campus Photo Hunt Text: Anouk Beursgens Signs (35) Buildings (47) Nature (65) Objects (74) Student house (45)

Solution: Numbers on the Table Text: Matthew Maat Answer: 6896551724137931. The word ‘table’ was a hint to look at the multiplication table. Each n-digit number from this sequence has the property, when we look at its first n multiples, that the digits of the multiples are cyclic permutations of each other. For example 142857, 285714, 428571, 571428, 714285 and 857142. This can only happen for numbers of the form

with p prime, with the

additional restriction that 10, 100, 1000,..., 10p-1 are all different modulo p. A proof outline: if m is our n-digit number, then we can look at

with gcd(a,b)=1. So the decimal expansion of a/b is just m written infinitely many times in a row. If we split off the first couple of digits of this expansion and assume that the remainder is a multiple of m written infinitely

many times, then we get

from which can be derived that 10x=d mod(b), and if there are numbers x such that this holds for d=1,2,...,n then b must be prime. If you found it just by educated guessing, still great job!

Barcode Puzzle Text: Timon Veurink The barcodes are dates encoded with the first number of the series. It is in the format of: Key mmyyyy mmyyyy. The idea is that you add the first number to the rest of the numbers. This gives you the following: 1 081771 121843 August 1771/December 1843 2 121792 031849 December 1729/March 1849 3 021817 111890 February 1817/November 1890 3 081880 111962 August 1880/November 1962 1 041909 032004 April 1909/March 2004 These are the lifetimes of the first 5 monarchs of the kingdom of the Netherlands. Willem 1, Willem 2, Willem 3, Wilhelmina and Juliana. This was also hinted at by the encoder numbers. 1 2 and 3 hint to Willem 1, 2 and 3. The following 3 and 1 are combined the dialling code of the Netherlands, +31. Therefore the answer would be the Dutch royals.

Solution: Battleship Text: Daan Pluister

Solution: Bermuda Triangle Text: Matthew Maat There are not too many routes that always work, but the ones that do work are routes that look like a long S- or Z-shape. For example, the route below works:

Even when you start on the worst spot as in the picture you still have a couple 100’s of meters left at the end when you escape. From: Conjecture 4.3, Rick Norwood, George Poole, Michael Laidacker. “The Worm Problem of Leo Moser.” Discrete & Computational Geometry (1992), vol. 7, pag. 153-162.

Solution: Chess Puzzles Text: Thomas Kanger Easy: Bb5+, Nc6, N*c6, b*c6, B*b6+, Bd7, B*a8. Medium: R*b2+, Ka1, Rb1+, K*b1, Qc2+, Ka1, Qb2#. Hard: Solution1: R*b2+, Q*b2, B*b2, R*b2, d2+, Rc2, Qb3+, Ka1, B*c2, anything, Qa3#. Solution 2: B*b2, Q*b2, R*b2+, R*b2, d2+, Rc2, Qb3+, Ka1, B*c2, anything, Qa3#.

Solution: Codebreaker Sudoku Text: Tim Hut

Using the number of symbols in the grid gives the word GATE, (since (3x2)+1=7=G; (2–1)+0=1=A; (6 x 3)+2=20=T; 2+2+1=5=E)

Solution: US vs UK Text: Jorn de Jong The answer is either 9:45:09 or 12.9495km/h. Both are correct.

Solution: Anagram Text: Anouk Beursgens The answer is 9/nine.

Solution: Keep the Chairman Healthy Text: Matthew Maat This problem is derived from the union closed sets conjecture, which is an interesting problem in set theory/ combinatorics. All the amounts are actually a)

the minimum possible amounts for their value of k. If you feel like doing so, try to prove this ;).

Possible answers are (where a number represents an M&M of the colour associated to that number):

Solution: Skyscrapers Text: Lavinia Lanting

Solution: Quotefall Text: Martijn ter Steege The AMW in twenty twenty one in Twente is twice the fun.

Solution: Logos Text: Sanne Oude Veldhuis Marlboro Ola Ubisoft Nestle Toyota Asics

Intersport National geographic Carrefour Leger des heils Ikea Martini

Bic Essent Rolex SP MOUNTAINCLIMBERS

Solution: Logiquiz Text: Marjolein Bolten

Solution: Killer Sudoku Text: Linda ten Klooster

Solution: Get the code! Text: Daan Velthuis

Solution: Word Search Text: Luuk van der Werf

Abacus – who are we? (6) Active – What are you too much when you suffer from ADHD? (6) Board – Who did organise this weekend, among others? (5) Boat – how do you get on Texel? (4) Campfire – where should you not fall in? (8) Coffee – what keeps you alive during the weekend (6) Committees – Big chance you were or are in one of these (10) Enschede – Where are we? (8) Flunkiebal – student’s favourite sport? (10) Grolsch – Your favourite beverage (7) Knakworst – Your favourite late-night snack (9) Mathematics – Your favourite high school course (11) Navy – which colour is very different from blue? (4) Swimming – Your favourite Sunday activity (8) Texel – Where would we be? (5) Train – Pluister’s favourite vehicle (5)

Solution: Penrose Tiling Slitherlink Text: Daan Pluister

Solution: Cryptic Crossmaths Text: Stefan Klootwijk Across 1 Rho 5 Epsilon 8 Divergence 9 Parallelogram 11 Phi 12 Event 13 Sums 14 Set 15 Frequencies 17 Remainder 21 Dot 22 Arc 23 Areas 24 Norms 25 Edges 26 System.

Down 1 Round 2 Odd 3 Inverse 4 Parallelepipeds 5 Element 6 Sectors 7 Omega 9 Point 10 Remainders 11 Postulate 16 Satisfy 18 Means 19 Disks 20 Range.

The letters in the lightly coloured squares are HMADLSOUIREMY, which is a perfect anagram of SUMMER HOLIDAY. For a detailed explanation of the solution, see https://sklootwijk. stackstorage.com/s/ Dy2qryZD82HqL9U

Solution: Eastereggs Text: Stefan Klootwijk Solution The first figure contains three (partially overlapping) ‘word snakes’: the red one spells the given text ‘This puzzle also contains some easter eggs.’; the blue one provides the clue ‘The answer is divisible by 12 according to a former chairman.’; and the yellow one is the random quote `The next station is gross was announced in the train.’ Note that an overlapping parts of the snakes are coloured appropriately: red+blue=purple, red+yellow=orange, blue+yellow=green and red+blue+yellow=black. This principle is also used in the other two figures. The second figure contains three (partially overlapping) QR codes. If you ‘split’ the colours, then they contain the following texts: ‘This puzzle also contains some Easter eggs.’ (red); ‘The Romans needed 10 symbols to write the anwer.’ (blue); and ‘It was neither 50 nor 51, remembered Justus Sleurink.’ (yellow). The

third figure contains three (partially overlapping) binary codes. If you ‘split’ the colours and let the columns correspond to binary numbers which in turn correspond to letters, you will find the following texts: ‘this puzzle also contains some easter eggs’ (red); ‘cas sitvast added two squares to obtain the answer’ (blue); and ‘go to an isle is almost correct wrote wout leemeijer’ (yellow). Combining the information from the three (blue) clues, you are left with the following nine numbers: 1872, 2088, 2448, 2628, 2880, 3528, 3636, 3744, 3816. Using the last bit of information, you will see that 2880 is the code that you had to find. Easter eggs Ae wwfgawg vrfdnew ghkgqoesf ig bvr ucesjs vxsqhq, hjekm oej atfc Snwtqn puis aqrqjv ng gh. Gle dwyrqm jccgj qs mfs smrep qwiukm (huj vjqr ggetuky wu gkwgf) bix fcoax ta ztfgcm gch nv yac rvveoptcp oy bv-

vssnge oosuf pss CMP. Bvr wiswma dyofad wp tam cgmmw muc smggnpg teymf fyztgezl xo fdp zqctbwbs wk mfwf cemn’d OOW (tthutcla gh’f vafdpf fiynwpzty mm gri ir uzi fog’b yate yac zbgafezb aem). Izft bmx qcyytuky hq taqg czheec wf rof ffgv a (lmav-)wiswmayc ctkdsp nnuprw, jzm gh eifqnd hq tam hbbv (shr hui mgjtqkpttwgd!) wk mfwf cemn’d qcmi tcpfbnhl tbv tta LAY (htds n qwtd yh vxs Pqeqj Wbswcjlnt noti azz jcw kgwk jmg…). Kbloypy, fdp qnux qb gmm kbpgg jisqcs eogbovsa f (yyf-sitodpr) jigb hb hwrijsgi tta wceamqca nvkhpanxiaj afqvblsq nv yac fnrdai biqtxa. Wg rqlar vrpp fk afqvbls gmm jqrfn mnrkcactbwb gmiy mfs vrifelzu oy bvr kwwfcf plaunxop akm K.E.

Roman Crossword Text: Stefan Klootwijk F = 79 (which is indeed a prime) G = 2000 > 1500 = H A + F = 3600 + 79 = 3679 and J + M = 2710 + 969 = 3679

Given the completed crossword, the first six clues are easy to validate: A = 3600 = 602 D = 1770 = 59*60/2 E = 216 = 63

The final clue has an extra catch: some of the letters here refer to crossword entries, whereas others are Roman numbers. This yields E + I + M = 216 + 3250 + 1000 = 4466 = 3640 + 100 + 100 + 626 = C +C+C+L

Solution: Big Logiquiz Text: Stefan Klootwijk

The solution can now be read in the bottom row (including the leading M): MCMLXIX, or 1969 if you’re not Roman.

Solution: Trains Text: Stefan Klootwijk This problem describes a real situation. The steam trains belong to the Harzer Schmalspurbahnen (Harz Narrow Gauge Railways) in Germany, the station under consideration is called Drei Annen Hohne, the main line runs from Nordhausen (left side) to Wernigerode (right side), and the branch line goes to the Brocken summit. The time table information corresponds to the actual time table at the time that the author visited this station. Although the following information was not available in advance, it also might help to realize that all three locomotives need quite some time (actually a little bit more than 10 minutes) to refill their water tanks at the station. Also, once you’ve seen the first step, it is not too difficult to sort out the remaining steps. The correct time line is as follows: 15:16 – Train 1 arrives from Nordhausen on platform 3; immediately after arrival its locomotive is being uncou-

pled from the train and being shunted to the water crane on platform 1, where it starts refilling its water tanks. 15:30 – The locomotive on platform 1 is now refilled with water and moves slightly forward in order to make sure that train 2 will fit on platform 1 and its locomotive can use the water crane. 15:32 – Train 2 arrives from Wernigerode on platform 1; its locomotive starts refilling its water tanks. 15:33 – Train 3 arrives from Brocken on platform 2; immediately after arrival its locomotive is being uncoupled from the train and being shunted to the water crane on platform 3, where it is being coupled to train 1 and starts refilling its water tanks. At the same time, the (refilled) locomotive on platform 1 that made some space for train 2 is being shunted to platform 2, where it is being coupled to train 3.

15:40 – Train 3 leaves from platform 2 towards Nordhausen. 15:46 – The locomotive in front of train 2 on platform 1 is now refilled with water; train 2 leaves from platform 1 towards Brocken. 15:50 – The locomotive in front of train 1 on platform 3 is now refilled with water; train 1 leaves from platform 3 towards Wernigerode. The coloured squares on the schematic track plan are signal flags. If you follow the path of each locomotive through the station, and collect the letters corresponding to the flags they pass (either partially or completely visible on the right side of the track), you obtain ‘wreigdnoeer’, ‘bnoerck’ and ‘hreousndna’, which are anagrams (hint: rearranging) of the end stations in each direction.

Solution: Geoguesser Sudoku Text: Daan Pluister

Solution: Puzzle Sequence Text: Daan Pluister