Puzzle Booklet 2022

Dear reader, after the great succes of the puzzle booklet we brought out last year, the Ideaal! has decided to, once again, make a puzzle booklet for you to enjoy during the summer while on vacation and, hence, far away from all of your favourite mathematicians and, of course, from your favour ite magazine!

Who knows, maybe last year, in spite of everything, was only the very beginning of what was to come for the Ideaal!.

With your support, we might be able to make a puzzle booklet every single year from now on, so make sure to send all of your puzzles next year!

In this year’s edition of the puz zle booklet you can find many puzzles made by both members of the Ideaal! and by many other

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 Eva van Laar Lavinia Lanting

members of Abacus. Jorn made some lovely frog puzzles, while Daan Pluister made a sequence puzzle for you to figure out. There are also have some classic nono grams, as well as chess puzzles. In addition, Jorg created a cross word in the style of your favourite TV show ‘Smarter by the Second’ and your movie knowledge will be tested through a quite peculiar anagram.

By bringing this puzzle booklet with you on vacation, a little piece of the Ideaal! and of our beloved association W.S.G. Abacus will always be there with you. Hopefully this little booklet will make your summer even better. Enjoy your well deserved rest and have a great summer!

The Ideaal!

Guest writers:

Jorn de Jong (Frog Sudoku, Frog Jumps, The Frog King), Daan Pluister (Sequence Puzzle), Matthew Maat (Checkmate in 2), 54th Board (AMW Puzzle), Candidate Board (‘Kandi’ Sudoku), Martijn ter Steege (Where does the King go?), Thomas Kanger (Letter Puzzle).

Connect the Dots

Text: Tim Hut

Frog Sudoku

Text: Jorn de Jong

A frog stumbles across a sudoku with one small twist; two cells connected by an edge can not have a difference of one.

For example, you will never see a 5 direct ly next to, above or below a 4.

Nonograms

Text: Lavinia Lanting

Sequence Puzzle

Text: Daan Pluister

Solve the puzzels in order. The Lat in letters, Roman numerals and Greek letters will be num bers which you have to use as a clue for the next puzzle(s).

11: The number in the square indicates how many squares are coloured in the adjacent (also diag onally and possibly including the square itself) squares.

12: Fill in each row and column the num bers 1,2 and 3 (so two squares remain blank per row/col umn). The number outside the grid indi cate which number can be seen first in the row/column.

21: The number in the square indicates how many blank squares it can see vertically and horizontally together, in cluding the cell itself. A coloured square blocks the view.

No two black squares may be touching vertically or horizontally.

22: The number in the square indicates how many borders the square should have. Make 7 rooms of equal size. A bor der may not end in a dead end.

31: The number in the square indicates how many borders the square should have. Make one room. A border may not end in a dead end.

32: Fill in each row and column the numbers 1,2,3,4,5. The number in the square indicates the height of the square. The numbers outside the grid indicate how many height eleva tions it can see in the row/column.

Checkmate in 2

Text: Matthew Maat Checkmate in 2 Checkmate in two puzzles.. easy, right? Here are twelve of the hardest checkmate They are all white to move, in somewhat increasing difficulty and of course, they 2 moves always need to give a check. Sometimes to find need to try many legal moves for white, even the ridiculous ones. Also, a common black in zugzwang (leave black only with bad moves). Finally, assume castling is rook are in the right spot. Good luck!

Checkmate in two puzzles...easy, right? Here are twelve of the hardest check mate in two puzzles. They are all white to move, in somewhat increasing difficulty and, of course, they are all checkmate in 2 moves.

Small tips: you don’t al ways need to give a check. Sometimes to find the solution you may need to try many legal moves for white, even the ridiculous ones. Also, a com mon theme is putting black in zugzwang (leave black only with bad moves). Finally, as sume castling is allowed if

king and rook are in the right spot. Good luck!

Frog Jumps

Text: Jorn de Jong

Twelve frogs arrive at the left bank of a riv er, all on a uniformly random place. They all decide to jump to the right bank, to an uniformly random place on that side.

AMW Puzzle

Text: 54th Board

How well do you know the current board members? Connect each board member to his or her hobbies and instruments they play (mul

The frogs wonder what the expected number of crossing (not considering the height) in their jumps will be. With this the frogs mean the expected number

of crossing of these twelve lines if you draw all jumps as lines between two line segments (the bank of the rivers).

tiple board members may share one hobby or instrument and all hobbies and instruments can be connected to at least one board member.

Finally, indicate on the given map of the Netherlands where each board member comes from.

The Frog King

Text: Jorn de Jong

In a land far away, a frog is king. Since a war against the herons is coming, the frog king wants as many frog girls to be ready to fight. Therefore he rules as follows:

1) All frog couples must create children until they get a baby frog girl, then they must stop creating children.

2) All frogs can only lay a single egg at a time, and they have to wait until it is fully hatched to lay a new one.

The frog king thinks that with these two rules, the ratio of frog girls to boys will increase drastically. When times goes to infinity, what is the ratio of frog girls to boys?

Summer without Clouds

Text: Daan van Kats

Summer is visible everywhere again. Some places in the Netherlands are at

their best when not a single cloud is visible in the sky.

Every frog baby has an equal probabil ity of being either gender.

Can you find out what location I am talking about?

‘Kandi’ Sudoku

Text: Candidate Board

Where does the King go?

Text: Martijn ter Steege

The following position can only be le gally reached for one position of the white king. Where can you place the white king and only the white king such that the

position can be reached legally?

Abaquiz Crossword

Text: Jorg Gortemaker

Do you think you got what it takes to participate in an episode of Smarter by the Second, link the hints to the answers and fill in the missing answer in the cross word. Good luck!

P.S. If you want to participate in season 3 message us at abaquiz@abacus. utwente.nl

Aerodynamic device, when placed in front of the car they are often called air dams.

Spindle

Gearbox Transmits and controls the propulsion power of the engine. Kingpin Main pivot of the steering mechanism of a car or other vehicle. Radiator Part of the suspension system that carries the hub for the wheel and attaches to the upper and lower control arms.

Text: Lavinia Lanting

I’m going to make you an offer you can’t refuse.

Before you are pic tures of iconic mo ments from famous and iconic films, the titles of which (excluding the spac es and symbols in between words, but including any num bers present in the

title) will be the guide towards the answer.

Do you know all of them?

Can you figure out what famous film quote is revealed through this anagram? And will you be able to recognise which film it comes from?

Good luck!

Letter Puzzle

Text: Thomas Kanger

Place the letters A-D exactly once in every row and column. Some cells remain empty.

Clues outside the grid indicate the first letter in that row or column as seen from that direction.

Solution: Connect the Dots

Text: Tim Hut

Solution: Frog Sudoku

Text: Jorn de Jong

Solution: The Frog King

Text: Jorn de Jong

Of course, this ratio is simply 1. Since the number of baby frog girls born is still the same as the number of baby frog boys born. If you don’t believe me (like some people in the

Abacus room :P), you can solve the expect ed number of baby frog boys and girls a frog couple has. Of course, the expected number of baby frog girls for a frog couple is 1. For baby frogs

boys, let E[M] be the expected number of baby frog boys a frog couple has, then this is 1 as well. Hence the ratio is (again) 1.

Solution: Frog Jumps

Text: Jorn de Jong

Any pair of two frogs have exactly a prob ability of a half of crossing and there are 12 choose 2 pair

of frogs. Therefore the expected number of crossing is a half times 12 choose 2, which is 33.

Solution: Checkmate in 2

Text: Matthew Maat

Puzzle 1: After 1.Ra6 either 1… bxa6 2. b7# or something like 1… Bc7 2. Rxa7#

Puzzle 2: After 1. Rg5 either 1…Kf8 2. bc5# or if the king goes to the 6 th rank Bd8 is mate

Puzzle 3: After 1. Rc3 either 1… b3 2. Rxc4# or 1..bxc3 2. Bc2#

Puzzle 6: Classic queen sacrifice and knight promotion: 1.Qd6+ Kxd6 2.fx e7=N#

Puzzle 7: 1.Qd5+ after which either Rb5, Nxd3 or Ne4 is mate

If black tries to stop that, we get 1…Kxf4 2. Qe3#, 1…Bxf4 2. Qc5#, 1..Rd4 2. Qe3# or 1…Kd5 2. Qc5#

Puzzle 4: We play 1. Ba1 to avoid stale mate and then 1… Kxa2 2. Qb2#

Puzzle 5: We hang all the pieces with 1. Qc6, after which black is in zugzwang, and on the next move either Qa4, Rd8, Qxc8, Qxc7, Ra6 or Rxa6 is mate

Puzzle 8: Black is in zugzwang after 1. Qb2. Moving the rook allows 2. Qh8#, moving the pawn 2. Qb7#, and mov ing the knight either 2.Kxd2# or even better 2. O-O-O#

Puzzle 9: 1.Rf6 puts black in zugzwang, after which 1…Kc5 2. Qxa7#, 1…Ke3 2.Qd3# or 1…Ke5 2.Qa1#

Puzzle 10: 1.Rd4 threatens 2.Qd4#.

Puzzle 11: 1. Rg7 and there are three different mates: 1… Kxc7 2. Rd5#, 1… Kd7 2.R4xe7# and 1…e6 2.c8=N#

Puzzle 12: 1. Qa5 and despite hav ing many possible moves, black is in zugzwang. Any move allows one of the moves Qxb4, Nf5, Qa1, Qd5, Qe5 or Qb6 with checkmate

Solution: Nonograms

Text: Lavinia Lanting

Solution: ‘Kandi’ Sudoku

Text: Candidate Board

Solution: AMW Puzzle

Text: 54th Board

Hobbies

Niels: horsebackrid ing, soccer, tennis, cycling, mountain biking, ice skating, running.

Thomas: soccer, (table) tennis, ice skating, running, cycling, chess.

Eline: athletics, survivalrun, crossfit. Margriet: (table) tennis, athletics, scouting.

Musical instruments Niels: recorder, gui tar, piano. Thomas: keyboard.

Eline: harp, violin, keyboard, flute. Margriet: keyboard, piano.

Places

Thomas: Hengelo. Eline: Zwolle. Niels: Harfsen. Margriet: Kampen.

Solution: Where does the King go?

Text: Martijn ter Steege

The position can only be reached if a few moves back the position looked like this. Then we have: c4 blocking the bish op check, bxc3 the black pawn takes the c-pawn en passant

resulting in double check, the white king takes on c3, leaving only the original piec es and a white king on the board giving us the solution, white king on c3.

Solution: Summer without Clouds

Text: Daan van Kats

Solution: Abaquiz Crossword

Text: Jorg Gortemaker

1 h o 2 k w 3 b a s e b a l l 4 o t e m 5 c a u c h y 6 e r i t 7 r e a m 8 c u n 9 r a d i a t o r m n r m d t y u e 10t r i f i d

Solution: Movie Anagram

Text: Lavinia Lanting

The number followed by a point tells you which word the letter belongs to, while the number in between brackets indicates which letter in the title of the movie you are looking for. Recognising all movies and correctly

placing each letter yields then the quote

“I won’t kill you be cause you’re just too much fun. I think you and I are destined to do this forever.”

This is a quote by Heath Ledger’s Joker from the second in stallment of Christo

pher Nolan’s Batman trilogy, ‘The Dark Knight’.

As for which movies I included? I’ll leave it up to you to figure out which one is which and if you hav en’t whatched some of them, I recom mend you do!

Solution: Letter Puzzle

Text: Thomas Kanger