Editors: Ninoslav Kunc i Petar Mladini´c WONDERFUL...iv The wonderful world of math 1.36. Can it be balanced? . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.37. How many

Editors: Ninoslav Kunc i Petar Mladinic

Petar Mladinic, Ninoslav Kunc:

The wonderful world of math

Zagreb, 2018.

Reviewers: Sanja Antolis, Jelena Gusic, Nikol Radovic

Editor: Ivana Babic

Proofreader: Nikol Radovic, Hrvoje Horvat

Proven Grupa d.o.o., Zagreb

c©Petar Mladinic i Ninoslav Kunc

This book or its parts may not be reproduced, stored or introduced into a retrieval system, or trans-

mitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise),

without the prior written permission of both the copyright owner and the publisher of this book.

CIP record for this book is available from the National and University Library in Zagreb

number 000982971

ISBN 978-953-7369-12-5

Syllable and page break: Petar Mladinic i Ninoslav Kunc

Print: Tiskara Zelina d.d.

Contents

The word, the two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1. Events and brain teasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1. Who has the advantage? . . . . . . . . . . . . . . . . . . . . . . . 4

1.2. How to divide fairly? . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3. How to apportion? . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4. Can you get 100? . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5. How to reach the goal? . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6. How much will it get? . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.7. Why the lawsuit is lost? . . . . . . . . . . . . . . . . . . . . . . . . 10

1.8. How late is the watch? . . . . . . . . . . . . . . . . . . . . . . . . 11

1.9. Who has brown eyes? . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.10. How old are they? English subtitle . . . . . . . . . . . . . . . . . 13

1.11. Does this geometric solid exist? English subtitle . . . . . . . . . . 14

1.12. Is it possible? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.13. What’s more? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.14. Does Ante know? . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.15. How long will the competition last? English subtitle . . . . . . . . 18

1.16. Who is whose? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.17. What time is it? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.18. How can the inheritance be split? English subtitle . . . . . . . . . 21

1.19. Does the embezzler have a fair trial? . . . . . . . . . . . . . . . . . 22

1.20. Can this problem be solved? English subtitle . . . . . . . . . . . . 23

1.21. Is it possible? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.22. Are the elephant and mosquito equal? . . . . . . . . . . . . . . . . 25

1.23. How much does the kitten eat? English subtitle . . . . . . . . . . 26

1.24. How to get rating four? . . . . . . . . . . . . . . . . . . . . . . . . 27

1.25. Who lies? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.26. Who does the judge trust? English subtitle . . . . . . . . . . . . . 29

1.27. What is the price? . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.28. How many of them are blood group 0? . . . . . . . . . . . . . . . . 31

1.29. What is more expensive? . . . . . . . . . . . . . . . . . . . . . . . 32

1.30. How long is the track? . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.31. Who knows how to count? . . . . . . . . . . . . . . . . . . . . . . 34

1.32. Will the dog catch a rabbit? . . . . . . . . . . . . . . . . . . . . . 35

1.33. Does the minister know how to count? . . . . . . . . . . . . . . . . 36

1.34. Do they know how to write? . . . . . . . . . . . . . . . . . . . . . 37

1.35. How deep is the marina? English subtitle . . . . . . . . . . . . . . 38

iv The wonderful world of math

1.36. Can it be balanced? . . . . . . . . . . . . . . . . . . . . . . . . . . 39

1.37. How many cases are there? . . . . . . . . . . . . . . . . . . . . . . 40

1.38. How do they look? . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

1.39. How much votes did he get? . . . . . . . . . . . . . . . . . . . . . 42

1.40. How many people are there? English subtitle . . . . . . . . . . . . 43

1.41. What is written on the paper? . . . . . . . . . . . . . . . . . . . . 44

1.42. How many apples are there? . . . . . . . . . . . . . . . . . . . . . 45

1.43. Can it be exchanged? English subtitle . . . . . . . . . . . . . . . . 46

1.44. How much will it cost? English subtitle . . . . . . . . . . . . . . . 47

1.45. How big is a settlement? . . . . . . . . . . . . . . . . . . . . . . . 48

1.46. Which offer is better? . . . . . . . . . . . . . . . . . . . . . . . . . 49

1.47. How many minutes does it take? . . . . . . . . . . . . . . . . . . . 50

1.48. Who is the weightlifter? . . . . . . . . . . . . . . . . . . . . . . . . 51

1.49. Who won? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

1.50. Who hit the center? . . . . . . . . . . . . . . . . . . . . . . . . . . 53

1.51. What does it say? . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2. Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Who has the advantage? . . . . . . . . . . . . . . . . . . . . . . . . . . 56

How to divide fairly? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

How to apportion? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Can you get 100? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

How to reach the goal? . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

How much will it get? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Why the lawsuit is lost? . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

How late is the watch? . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Who has brow eyes? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

How old are they? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Does this geometric solid exist? . . . . . . . . . . . . . . . . . . . . . . . 61

Is it possible? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

What’s more? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Does Ante know? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

How long will the competition last? . . . . . . . . . . . . . . . . . . . . 63

Who is whose? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

What time is it? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

How can the inheritance be split? . . . . . . . . . . . . . . . . . . . . . 65

Does the embezzler have a fair trial? . . . . . . . . . . . . . . . . . . . . 65

Can this problem be solved? . . . . . . . . . . . . . . . . . . . . . . . . 67

Is it possible? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Are the elephant and mosquito equal? . . . . . . . . . . . . . . . . . . . 68

How much does the kitten eat? . . . . . . . . . . . . . . . . . . . . . . . 69

How to get rating four? . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Who lies? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Who does the judge trust? . . . . . . . . . . . . . . . . . . . . . . . . . 71

What is the price? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

v

How many of them are blood group 0? . . . . . . . . . . . . . . . . . . . 72

What is more expensive? . . . . . . . . . . . . . . . . . . . . . . . . . . 72

How long is the track? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Who knows how to count? . . . . . . . . . . . . . . . . . . . . . . . . . 73

Will the dog catch a rabbit? . . . . . . . . . . . . . . . . . . . . . . . . 74

Does the minister know how to count? . . . . . . . . . . . . . . . . . . . 75

Do they know how to write? . . . . . . . . . . . . . . . . . . . . . . . . 75

How deep is the marina? . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Can it be balanced? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

How many cases are there? . . . . . . . . . . . . . . . . . . . . . . . . . 78

How do they look? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

How much votes did he get? . . . . . . . . . . . . . . . . . . . . . . . . 79

How many people are there? . . . . . . . . . . . . . . . . . . . . . . . . 80

What is written on the paper? . . . . . . . . . . . . . . . . . . . . . . . 80

How many apples are there? . . . . . . . . . . . . . . . . . . . . . . . . 80

Can it be exchanged? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

How much will it cost? . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

How big is a settlement? . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Which offer is better? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

How many minutes does it take? . . . . . . . . . . . . . . . . . . . . . . 85

Who is the weightlifter? . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Who won? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Who hit the center? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

What does it say? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3. List of brain teasers toward its content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4. Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5. Note about authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

vi The wonderful world of math

vii

The word, the two . . .

For most primary and secondary students in Croatia mathematics is traditionally unpopular

subject. Many of them have experienced it as arid, boring tiresome and difficult, but there

is a rationally small number of students who see and feels mathematics as beautiful, exciting

and seminal. Reasons which still led to such views resides not within mathematics itself: they

are in curricula and programs shortcomings and inadequacy, in textbooks and within some of

the teachers.

One of the most prominent Croatian high school teachers and math textbooks authors,

Stjepan Skreblin, used to say that for the successful mastery of mathematics students did not

need special talent, but they should not only be exceptionally talentless. A good math teacher

will know how to interests his students about it, who will always anxiously expect and with

the joy of creating participate in solving math tasks and problems.

This book of math comics is on the trails of attempts to increase understandings and

interests for mathematics. It was created based on a multi-annual section of comics (back

page) in magazine for young mathematicians Matka. It is in accordance with decision of 1st

congress of Croatian math teachers about math popularization, and as idea illustration that

math is always around us, in different situations. It is modest contribution towards standards

achievements published in Standards for teaching math.

The Wonderful World of ”Math” can be used as introduction stories or problems in teach-

ing new subject areas or differently. Parents may use stories to better understanding what

their children have been taught. For that purpose at the end of the book, stories are listed as

Number systems, Divisibility, Equations and Inequalities, Percentage, Diophantine equations,

Algebraic expressions, Logical tasks, Dirichlet’s rule (condition), Geometry, Graphs, Combi-

natorics, Probability and Statistics, and Ingenuity.

Comics’ lyrics were developed as dialogs that lead the reader from one problem to another.

Tasks and problems are chosen as easier and more difficult, more or less easy formulated,

discussed and solved, which allows the young reader to develop experience for the richness and

diversity of mathematics problems. For the advanced reader, it will be a stimulus for solving

tasks as well as creating own.

The book is designed as adventures and puzzles of school group students. Author’s ideas

are portrayed and characters are revived by Ninoslav Kunc. Kunc is by modifying characters

and commenting together with introducing minor characters/icons into original story gave

extra dimension and atmosphere. His comments are humorous and ironic in a positive sense

and by themselves are giving more lifelike frames to puzzles.

Problems are integrated into the possible realistic environment, but every reader realizes

that they are imaginary, i.e. that such reality does not exist.

Fundamental problem ideas are authorized or spotted in listed literature, with special

ideas selection from math history. Fundamental idea elaboration, text shaping’s and comic

illustrations are solely authors creations.

viii The wonderful world of math

In Croatian, nor in world literature, there is not such comprehensive attempt to make

mathematical problems in the form of comics.

There are attempts to classically write stories/novels in which mathematical problems

are present and their resolutions are main characters marginal activities. One of such rarely

attempt is book Stripologikon of Apostolos Doxiadis, Christos H. Papadimitriou and Alecos

Papadatos, in which the story of a modern mathematical logic and actors of its construction

was told in the form of a comic. And that is all.

Comic book The Wonderful world of Math includes new problems selection and it is natural

continuation of published book Adventures and puzzles of the Matka kids fellowship, written

by Petar Mladinic and illustrated by Zrinka Ostovic.

Given problem-story is usually frame in which eventually mode solving need to think

of, together with introducing new conditions which can help problem-solving (or cannot be

resolved).

Towards end of the book there is story list created accordingly to math subjects. List serves

reader as potential solving direction but also to teacher as orientation for introduction stories

or problems in teaching new subject areas.

In the end, sources and references for stories inspiration are listed.

With their reviews, text corrections and advices prof. Sanja Antolis, prof. Jelena Gusic,

and mr.sc. Nikol Radovic helped substantially.

Mr.sc. Nikol Radovic with her proofreading’s solutions substantially improved this book,

while prof. Sanja Antolis and prof. Jelena Gusic with their problem solutions examination

eliminated great portion of potential uncertainties, but also suggested a series of more simple

solutions.

To all of them, I thank heart fully!

I am also thankful to readers whom will, reading and solving this puzzles, point out errors

or better and more beautiful solutions, which I hope will be implemented in next edition of

The Wonderful world of Math.

[email protected]

Masta je vaznija od znanja.

Albert Einstein

Dijete je vatra koju treba razbuktati, a ne posuda koju treba napuniti.

Aristotel

Ante, Ivan, Luka, Jurica i Danica ucenici su jedne zagrebacke skole i glavni su likovi ove

nase price. Slicni su djevojcicama i djecacima u nama i oko nas. Dobri su prijatelji, sportasi i

streberi, mangupi i intelektualci. I stalno im se dogadaju neke zanimljive zgode. A ako im se

i ne dogode, sami ih smisljaju i izmisljaju, i tako im nikad nije dosadno. A susrest cemo ih u

razredu, na ulici, u trgovini, u stanu, na trznici, u knjizari, na moru. . .

Uz njih cemo upoznati i jos neke ucenike iz razreda: Kresimira, Vinka, Tomislava, Petra;

profesore Matka i Eugena; susjeda Martina; trgovce Marka i Anu; Antinu baku Maricu i djeda

Antu; podvornika Jozu. . .

Sigurno cete zajedno s njima uspjeti rijesiti sve matematicke probleme, a mozda i sami

smisliti neke nove zadatke za neku drugu pricu.

Evo nekih spomenutih Matkaca:

2 The wonderful world of math

reklama

1. Events and brain teasers


1.1. Who has the advantage?

Rjesenje je na stranici 56.

1. Events and brain teasers 5

1.2. How to divide fairly?



1.3. How to apportion?



1.4. Can you get 100?



1.5. How to reach the goal?



1.6. How much will it get?



1.7. Why the lawsuit is lost?



1.8. How late is the watch?



1.9. Who has brown eyes?



1.10. How old are they? English subtitle

The solution is on the page 61.


1.11. Does this geometric solid exist? English subtitle



1.15. How long will the competition last? English subtitle


2. Solutions


Tko ima prednost? (Who has the advantage?)

Uvijek pobjeduje drugi igrac sa sljedecom strategijom:

drugi igrac precrta ostatak reda (nakon sto je prvi igrac precrtao od 1 do 9 kvadratica).

Prvi je poceo Ivan. U ovoj igri obojica su igraca pogrijesila. Prvo je pogrijesio Luka jer u

drugom redu nije isao do kraja retka, a onda Ivan jer u cetvrtom redu nije isao do kraja retka.

Dakle, mogli su igrati bolje.

Kako posteno podijeliti? (How to divide fairly?)

Tri su prijatelja putovala jos 11 dana i potrosila 11 000 eura - svaki po11 000

3eura.

Marko je imao 7 000 =21 000

3eura i od toga iznosa potrosio je na sebe

11 000

3eura, a na

Jerka preostalih10 000

3eura.

Petar je imao 4 000 =12 000

3eura i od toga iznosa potrosio je na sebe

11 000

3eura, a na

Jerka preostalih1 000

3eura.

Jerko je, dakle, ”posudio” od prijatelja10 000

3+

1 000

3=

11 000

3eura.

Marko i Petar trebaju podijeliti iznos od 11 000 eura, koji im je nakon putovanja dao Jarko,

u omjeru njihove ”posudbe”. Marko je ”posudio” Jerku 10 puta veci iznos nego je to ucinio

Petar.

Dakle, Marko treba dobiti 10 000 eura, a Petar 1 000 eura. Markov je zahtjev posten!

Kako razdijeliti? (How to apportion?)

Lopta je stajala 450 kn. Svaki bi Matkac trebao platiti 112, 5 kn.

Iz izjava Matkaca mozemo sastaviti sustav linearnih nejednadzbi gdje su j, i, l iznosi koje

su za kupovinu lopte dali Jurica, Ivan i Luka.

j + i + l = 450 . . . cijena lopte

j ≤ i + l . . . Jurica

2i ≤ j + l . . . Ivan

5l ≤ j + i . . . Luka

Iz prve jednakosti izracunamo redom i + l, j + l te j + i.

Dakle, iz j + i + l = 450 slijedi da je

i + l = 450− j,

j + l = 450− i,

j + i = 450− l.

3. List of brain teasers toward its content


Kao mogucu pomoc u snalazenju evo vam, na kraju, ovaj popis zgoda i mozgalica prema

matematickim podrucjima.

1. Brojevni sustavi - Numerical systems:

• 1.8. Koliko kasni?(How late is the watch?)

• 1.21. Je li moguce? (Is it possible?)

2. Djeljivost - Divisibility:

• 1.4. Moze li se dobiti 100? (Can you get 100?)

• 1.14. Zna li Ante? (Does Ante know?)

• 1.16. Tko je ciji? (Who is whose?)

3. Jednadzbe i nejednadzbe, postotak - Equations and Inequalities, Percentage:

• 1.3. Kako razdijeliti? (How to apportion?)

• 1.7. Zasto je parnica izgubljena? (Why the lawsuit is lost?)

• 1.16. Tko je ciji? (Who is whose?)

• 1.19. Ima li pronevjeritelj posteno sudenje? (Does the embezzler have a fair trial?)

• 1.20. Moze li se rijesiti kucni problem? (Can this problem be solved?)

• 1.21. Je li moguce? (Is it possible?)

• 1.23. Koliko macic pojede? (How much does the kitten eat?)

• 1.27. Kolika je cijena? (What is the price?)

• 1.31. Tko zna racunati? (Who knows how to count?)

• 1.32. Hoce li pas uloviti zeca? (Will the dog catch a rabbit?)

• 1.33. Zna li ministar racunati? (Does the minister know how to count?)

• 1.36. Moze li se uravnoteziti? (Can it be balanced?)

• 1.39. Koliko je dobio glasova? (How much votes did he get?)

• 1.46. Koja je ponuda bolja? (Which offer is better?)

4. Diofantske jednadzbe - Diophantine equations:

• 1.40. Koliko je osoba?

(How many people are there?)

• 1.42. Koliko ima jabuka?

(How many apples are there?)

• 1.43. Moze li se razmijeniti?

(Can it be exchanged?)

3. List of brain teasers toward its content 91

5. Algebarski izrazi - Algebraic expressions:

• 1.22. Jesu li slon i komarac jednaki?

(Are the elephant and mosquito equal?)

6. Logicki zadatci - Logical tasks:

• 1.9. Tko ima smede oci? (Who has brown eyes?)

• 1.24. Kako do cetvrtice? (How to get rating four?)

• 1.25. Tko laze? (Who lies?)

• 1.26. Kome vjeruje sudac?

(Who does the judge trust?)

• 1.48. Tko je dizac utega?

(Who is the weightlifter?)

7. Dirichletovo pravilo - Dirichlet rule:

• 1.15. Koliko traje natjecanje? (How long will the competition last?)

8. Geometrija - Geometry:

• 1.38. Kako izgledaju? (How do they look?)

• 1.45. Koliko je veliko naselje? (How big is a settlement?)

• 1.5. Koliko je do cilja? (How to reach the goal?)

• 1.11. Postoji li tijelo? (Does this geometric solid exist?)

• 1.29. Sto je skuplje? (What is more expensive?)

• 1.30. Koliko je duga staza? (How long is the track?)

• 1.35. Koliko je duboka lucica? (How deep is the marina?)

9. Grafovi - Graphs:


• 1.24. Kako do cetvrtice? (How to get rating four?)

10. Kombinatorika - Combinatorics:

• 1.6. Koliko ce dobiti? (How much will it get?)

• 1.37. Koliko ima slucajeva? (How many cases are there?)

• 1.44. Koliko stoji popravak? (How much will it cost?)

• 1.47. Koliko treba minuta? (How many minutes does it take?)

• 1.49. Tko je pobijedio? (Who won?)


11. Vjerojatnost i statistika - Probability and statistics:

• 1.10. Koliko ima godina? (How old are they?)

• 1.12. Je li to moguce? (Is it possible?)

12. Domisljatost - Ingenuity:

• 1.1. Tko ima prednost? (Who has the advantage?)

• 1.2. Kako posteno podijeliti? (How to divide fairly?)

• 1.13. Cega ima vise? (What’s more?)


• 1.17. Koliko je sati? (What time is it?)

• 1.18. Kako podijeliti nasljedstvo? (How can the inheritance be split?)

• 1.28. Koliko ih ima krvnu grupu O? (How many of them are blood group 0?)

• 1.31. Tko zna racunati? (Who knows how to count?)

• 1.34. Znaju li pisati? (Do they know how to write?)

• 1.41. Sto pise na papiru? (What is written on the paper?)

• 1.44. Koliko stoji popravak? (How much will it cost?)

• 1.47. Koliko treba minuta? (How many minutes does it take?)

• 1.50. Tko je pogodio u sridu? (Who hit the center?)

• 1.51. Sto pise? (What does it say?What does it say?)

4. Literature

1. Bunt, L. N. H.; Jones, P. S.; Bedient, J. D. (1976): The historical roots of elementary mathematics,

Dover, New York.

2. Castello, M. J. (1998): The Greatest Puzzles of All Time, Dover, New York.

3. Cistjakov, V. D. (1978): Starnie zadaci po elementarnoi matematike, Visa skola, Minsk.

4. Dalle, A. (1988): 2000 Theoremes et Problemes de Geometrie avec Solutions, Namur, Seilles.

5. Dejic, M.; Dejic, B. (1987): Zanimljivi svet matematike, Tehnicka knjiga, Beograd.

6. Devide, V. (1988): Zabavna matematika, Skolska knjiga, Zagreb.

7. Dudeney, H. E. (1958): Amusements in Mathematics, Dover, New York.

8. Dorrie, H. (1965): 100 Great Problems of Elementary Mathematics, Dover, New York.

9. Ferachoglou, R.; Lafond M. (2002): 100 friandises mathematiques, Ellipses, Paris.

10. Friedland, A. J. (1970): Puzzles in Math and Logic, Dover, New York.

11. Fourrey, E. (2001): Recreations arihmetiques, Vuibert, Paris.

12. Fourrey, E. (2001): Curiosites geometriques, Vuibert, Paris.

13. Gardiner, T. (2002): Mathematical challenge, Cambridge University Press, Cambridge.

14. Gardiner, T. (2000): Maths challenge 1, 2, 3, Oxford University Press, Oxford.

15. Gardner, M. (1959): Mathematical Puzzles and Diversion, Penguin Book, London.

16. Gardner, M. (1959): Mathematical Puzzles of Sam Loyd, Dover, New York.

17. Gardner, M. (1960): More Mathematical Puzzles of Sam Loyd, Dover, New York.

18. Gardner, M. (1956): Mathematiccs, Magic and Mystery, Dover, New York.

19. Gik, E. J. (1987): Zanimatelnije matematiceskie igri, Znanie, Moskva.

20. Giovanangeli, B. (2004): 100 Enigmes de geometrie, Eureka, Paris.

21. Ignatev, E. J. (1978): V carstve smekalki, Nauka, Moskva.

22. Klepic, D. (1972): Zabavna matematika, Tehnicka knjiga, Zagreb.

23. Konforovic, A. G. (1987): Matematika labirinta, Radjanska skola, Kiev.

24. Kordemsky, B. (1971): The Moscow Puzzles, Dover, New York.

25. Kordemskii, B. A. (1956): Matematiceskaja smekalka, Gosud. izdat. tehniko-teoreticeskoi litera-

turi, Moskva.

26. Kostic, Z. (1970): Izmedu igre i matematike, Tehnicka knjiga, Beograd.


27. Lehmann, J. (1980): Kurzweil durch mathe, Urania, Leipzig.

28. Libbrecht, U. (1973): Chinese Mathematics in the Thirteenth Century, Dover, New York.

29. Loyd, S. (1982): Male price za bistre glave, Sportska tribina, Zagreb.

30. Maxwell, E. A. (2006): Fallacies in Mathematics, Cambridge University Press, Cambridge.

31. Modenov, P. S. (1957): Sbornik zadac po specialnomu kursu elementarnoi matematiki, Sovetskaja

nauka, Moskva.

32. Olehnik, S. N.; Nesterenko, J. V.; Potapov, M. K. (1985): Starinie zanimatelnie zadaci, Nauka,

Moskva.

33. Pappas, T. (2009): The Mathematics Calendar 2009, Wide World Publishing/Tetra, San Carlos.

34. Pappas, T. (2008): Mathematical Snippets, Wide World Publishing/Tetra, San Carlos.

35. Perelman, J. I. (1974): Zivaja matematika, Nauka, Moskva.

36. Perelman, J. I. (1974): Zanimatelnaja algebra, Nauka, Moskva.

37. Perelman, J. I. (1972): Zanimatelnie zadaci i opiti, Detskaja literatura, Moskva.

38. Petrovic, L. (2006): Golovolomki i zanimatelnie zadaci, Nauka, Moskva.

39. Petrovic, M. (1985): Zanimljivi matematicki problemi, Naucna knjiga, Beograd.

40. Polonijo, M. (1979): Matematicki problemi za radoznalce, Skolska knjiga, Zagreb.

41. Polonijo, M. (1995): Matematicke razbibrige, Element, Zagreb.

42. Schuh, F. (1968): The Master Book of Mathematical Recreations, Dover, New York.

43. Smith, D. E.; Mikami, J. (2004): A history of Japanese mathematics, Dover, New York.

44. Smith, L. D. (1943): Cryptography The Science of Secret Writing, Dover, New York.

45. Steinhaus, H. (1958): Sto zadan, Panstwowe wydawniectwo naukowe, Warszawa.

46. Sapiro, S. J. (1984): Resenie logiceskih i igrovih zadac, Radio i svjazi, Moskva.

47. Thepault, L. (2008): Le chat a six pattes et autres casse-tete, Dunod, Paris.

48. Townsed, Ch. B. (1976): Merlin’s puzzle pestimes, Dover, New York.

49. Trigg, Ch. W. (1967): Mathematical Quickies, Dover, New York.

50. Tahan, M. (2003): Covjek koji je brojio, Izvori, Zagreb.

4. Literature 95


5. Note about authors

Ninoslav Kunc roden je 1957. u Zagrebu. Tijekom svoje umjet-

nicke karijere objavio je velik broj stripova, ilustracija, a bavio se i

dizajnom, te animiranim filmom. Ilustrirao je brojne udzbenike za

osnovnu i srednju skolu koji su se tiskali u milijunskim nakladama,

vise prirucnika, rjecnika i drugih izdanja vezanih za obrazovanje.

Knjiga za djecu koje je ilustrirao toliko je da ih odavno ne zna

nabrojiti. Desetljecima je suradivao s mnogim casopisima za djecu

i mlade, ponajvise s Modrom lastom, Smibom i Matkom.

Ilustrator je iznimne osjecajnosti i prepoznatljivog stila. Jedan je od rijetkih ilustratora

koji svoj crtez, prozet humorom, zna pribliziti djetetu a da pritom nista ne gubi na likovnosti

i minucioznoj perfekciji koja je svojevrsni zastitni znak ovoga darovitog umjetnika.

Ilustrirao je niz poznatih djecjih klasika koji su neizbjezni dio lektire. Neke naslove, poput

Petrice Kerempuha Slavka Mihalica i Bon - ton Zvonimira Baloga, ilustrirao je u vise navrata

za razlicite izdavace. Svako od ta dva izdanja (objavljena po tri puta) nastojao je dodatno

likovno obogatiti, sto je uvijek poseban izazov za ilustratora.

Svoje radove Ninoslav Kunc izlagao je na mnogim skupnim i samostalnim izlozbama, a

dobitnik je i vise nagrada za svoj rad.

Svoju strip djelatnost Kunc je profesionalno zapoceo jos sedamdesetih godina u casopisu

Polet. Bio je clan kultne grupe Novi kvadrat koja je unijela dasak svjezine u tradicionalnu

strip scenu. Stripom se kontinuirano bavi sve do danas, a poseban izazov bile su mu serije za

najmladu publiku.

U suradnji s profesorom povijesti Petrom Bucevicem objavio je knjige 100 slavnih izreka

i Anegdote o slavnim osobama, a u izdanju udruge Strip forum objavljena je zbirka njegovih

stripova Najzabavnije Kuncutarije.

Ninoslav Kunc godinama ilustrira i oblikuje matematicke casopise Matka i Poucak.

U suradnji s profesorom Petrom Mladinicem smislja stripove koji krase zadnju stran-

icu Matke. Te matematicke zagonetke u stripu jedan su od njenih prepoznatljivih zastitnih

znakova. Ova duhovita serija, koja izlazi godinama, na koncu je zasluzila da bude malo dot-

jerana i objavljena u knjizi.

* * * * *

Petar Mladinic roden je 1950. godine u Zagrebu, gdje je diplomi-

rao matematiku na Prirodoslovno-matematickom fakultetu.

Njegov rad ima dugotrajan ucinak na poboljsanje odgojne i

obrazovne prakse. Kao voditelj Nastavne sekcije Hrvatskoga

matematickog drustva pridonosio je razvoju profesionalnih potreba

ucitelja/nastavnika, ucenika i studenata u formalnome i neformal-

nome svakidasnjem i cjelozivotnom ucenju i poucavanju.

Organizirao je vise od 150 predavanja, mnogobrojne radionice, pokrenuo Ljetnu skolu

Rudera Boskovica te Ljetnu skolu V. gimnazije i HMD-a.

Za profesionalne potrebe ucitelja, ucenika i studenata utemeljio je cetiri matematicka

casopisa: Poucak, Matka, Playmath i math.e te inicirao izdavanja knjiga u sklopu Male

matematicke i Matkine biblioteke.

Napisao je stotinjak strucnih clanaka, knjiga, udzbenika, prijevode knjiga te organizirao

na desetke radionica za nastavnike i ucenike.

Pridonio je razvoju sustava obrazovanja u matematickom podrucju kao clan Vijeca za

nacionalni kurikulum i clan Radne skupine za izradu Nacionalnoga okvirnog kurikuluma za

matematiku.

Godine 2011. prijavio je projekt V. gimnazije IPAQ Peta - afirmativna nastava i inovativno

poucavanje u gimnazijama u okviru HKO koji je realiziran s timovima cetiriju gimnazija: iz

Vukovara, Pakraca, Knina i Metkovica te Prirodoslovno-matematickim fakultetom iz Zagreba,

uz sudjelovanje 1 200 ucenika i 1 000 nastavnika.

Osmislio je i organizirao projekt dvogodisnjih okupljanja ucitelja i nastavnika matematike

(susreti i kongresi nastavnika matematike) na kojima su izlagali hrvatski nastavnici, kao i

najugledniji strani strucnjaci iz podrucja nastave matematike.

Utemeljio je hrvatski ogranak TTT (Teacher Teaching Technology).

Utemeljio je i vise godina vodio Geometrijske radionice HMD-a.

Kao nastavnik, a posebno kao ravnatelj V. gimnazije, aktivno je bio ukljucen u zajednicu,

osnazivao demokratske procese, toleranciju i solidarnost medu mladim ljudima i njihovim

roditeljima.

U slobodnom vremenu bavio se i sudenjem rukometnih utakmica. Prvi je hrvatski

medunarodni sudac koji je licencu postigao u Lijepoj Nasoj. Od 1993. - 1999. godine bio

je clan tzv. elitne liste sudaca IHF-a (International handball federation). Sudio je utakmice na

Olimpijadi u Atlanti, 4 svjetska prvenstva, 3 europska, 2 azijska i mediteranske igre. Sudio je

zavrsnu utakmicu japanskog prvenstva kao i tuniskog. Takoder je sudio 7 zavrsnih utakmica

europskih kupova, utakmice na dva svjetska kupa te prvi europski super kup. Na obiljezavanju

100 godina sporta u Austriji sudio je utakmicu izmedu zenskih reprezentacija Austrije i Svijeta.

Ukupno je sudio vise od 250 medunarodnih utakmica.

Odlikovan je Spomenicom Domovinskog rata 1990.–1992., odlicjem Red hrvatskog pletera

i dobitnik je nagrade Ivan Filipovic.

Documents

Editors: Ninoslav Kunc i Petar Mladini´c WONDERFUL...iv The wonderful world of math 1.36. Can it be balanced? . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.37. How many