Logic Puzzles 3 by Kreativni centar

9 788652 907410

LOGIC PUZZLES BOOK#3

ree a series of th in d ir th e th his is ho enjoy at readers w ms. books aimed g math proble in lv so d n a s math challenge d trusty, old n fi ill w u o y , inHere ous fresh bra ri a v o ls a t u e path problems, b n seem like th e ft o ill w t I . twisters tle traps simple, but lit is n o ti lu so work to you’ll need to – p e st ry e v nd out lurk at e e harder to fi tl lit a in ra b r you e these nswer. To solv the correct a ledge ed basic know e n ’ll u o y s, m proble cs. of mathemati

BOOK #

CONTENTS I. CASES FROM THE OLD ATTIC

...7

II. PROBLEMS FOR THE ROOKIE DETECTIVE III. DETECTIVE TALES IV. ANSWER KEY

...27 ...61

...15

Šimon A. Đarmati BOOK #

#illustrations

LUKA DEJANOVIĆ

For Mila

Hmmm… Let me check FOREWORD Everyone has at least once been in a situation where you singlehandedly untangled a seriously tangled situation, a puzzling problem or a mind-bending riddle; found a key to the solution. Satisfied with yourself, you would then explain: ‘Oh, that’s nothing! I’ve got the brains, me!’ This statement does not only apply to the end result of the problem. Getting to it was also helped by your previous knowledge, but also skills that allowed you to utilize that knowledge. It was also important to correctly identify the problem, to spot where the issue lies, to figure out what’s the catch. After several somewhat unsuccessful attempts, different approaches, various paths towards the goal, as well as persistence or even audacity – why not? – you took a completely new road and reached success! Despite all your humility, you were, of course, visibly pleased with yourself. It is precisely this sense of satisfaction that was the catalyst for presenting you with this book. In fact, not just one book, but three of them, whose diverse activities will attract all those who are curious and persistent. Savour the joy of problem solving! Author

I I CASES FROM THE OLD ATTIC

I CASES FROM THE OLD ATTIC

1. CHILDREN IN A STRANGE MAN’S LAP

Children were waiting in line with

adults. The children would then sit on the man’s lap while their mothers took pictures. If a child was crying, the man would try to comfort them before their mother snapped the photo. What is this all about? 2. ALONE ON AN ISLAND

A man is all alone on an island,

without any food or water. And yet, he was not in fear for his life. Why? 3. WINNER WITHOUT A TROPHY

Despite winning the race, Buddy didn’t get a trophy. Why?

4. HIGH-RISE TENANT

A man lived in an apartment located

on the twelfth floor. Every day, he

BOOK #

would take the elevator to the ground floor, then leave the building. In the evening, when returning from work, he would only take the elevator up to his apartment if there was another person in it or if it was raining. Otherwise, he would ride it to the tenth floor, then climb the stairs to the twelfth floor. Why did he do this? 5. STRANGE BARTENDER

A man walked into a bar and asked for a drink. Having heard this, the bartender pulled a gun and pointed it at the man. The man then said: “Thank you,” and went outside. What is this all about? 6. UNTIL THE PHONE RINGS

A man was lying awake in bed. He called somebody on the phone. He said nothing, then fell asleep. What is this all about?

I CASES FROM THE OLD ATTIC 7. A SPY’S SWIFT ARREST

Hans and Fritz were German spies

during World War II. They tried to enter the United State by posing as American tourists returning from holiday. Hans was immediately arrested. Based on what?

8. UNUSUAL OBJECTS IN MR. SMITH’S GARDEN

A carrot, pieces of coal, a broken pot and a pipe were lying in the middle of the garden in front of Mr. Smith’s house. What was this all about? 9. TOURING FOREIGN COUNTRIES IN ONE DAY

An ordinary American citizen

visited 30 foreign countries in a single day without a passport. He received warm welcome in each country and left of his own will. How was this possible?

10. DRIVING ON THE HIGHWAY

A man was driving on the highway at the speed of 90 km/h. He drove past three vehicles that were moving at the speed of 100 km/h. He was pulled over and fined by the traffic police. Why? 11. LEAVING THE ROOM

A man left his motel room, got into

a car, honked and came back. Why? 12. TYING UP PETE

One of the people who loved Pete

the most tied him to a seat, but Pete wasn’t worried. Why was Pete tied?

13. APPROACHING THE STATION

A train was approaching the station. Passengers who waiting for the train weren’t moving. What is this all about? 14. COLOURFUL HOUSES

One house is RED, one BLUE, and

one WHITE. If the RED HOUSE is left to the house in the middle, and the BLUE HOUSE is right to the house in the middle, where is the WHITE HOUSE?

BOOK #

I CASES FROM THE OLD ATTIC 15. LETTERS IN A ROW

Which letters should be placed at the end of the row? J, F, M, A, M, J, J, A, _, _, _

16. MOTHER OF FOUR

George’s mother has four children.

She named the first child Monday, the second child Tuesday, and the third child Wednesday. What is the fourth child called? 17. MIKE THE BUTTERFLY

Even though Mike the Butterfly didn’t possess any superpowers, he could predict the score of every football game before the kickoff. How? 18. IN THE OCEAN

Imagine you’re on a boat in the middle of a choppy ocean. You are suddenly surrounded by a number

of hungry sharks who can’t wait to devour you. How do you find your way out of this hopelessly difficult situation? 19. HOLD IT

What can you hold without touching it?

20. PAUL THE WAITER

A man walked into a restaurant. Paul the Waiter told him: “Good day, admiral!” Why did the waiter use the word “admiral” to address this man? 21. THE BICYCLE RACE

You are competing in a bicycle race.

You took over the runner-up just before the finish line. In which place did you finish the race? 22. THE PHOTOGRAPH

A man is looking at a photograph.

His friend asks him who is in it. “I don’t have any siblings. But the father of the man in the photograph is the son of my father.” Who is in the photograph? 23. HIGH SOCIETY

Arnold Schwarzenegger’s is long.

Nu’s is short. Madonna doesn’t use

BOOK #

I CASES FROM THE OLD ATTIC hers. James Bond always uses his. The Pope never uses his. What is it? 24. ONE HAPPY FAMILY

Your parents have six sons, inclu

ding you, and each one has a sister. How many people are in this family? 25. GUESS THE LETTER

Which letter comes next? D, R, M, F, S, L, S, _

26. SUBTRACTION

How many times can you subtract 2 from 50?

27. THE DIGIT 3

If you write all numbers from 300

are telling the truth, who is the actual robber? 30. OCTOBER REVOLUTION

When do Russians commemorate

the October Revolution: in October, November or December?

31. MR. JONES’ AGE

“How old are you, Mr. Jones?”

“I will tell you this much: my brother is two years older than me, and my sister is six years older than me. My mother was 20 when she had me, and I mentioned just yesterday that the average age between the four of us is 39.” How old is Mr. Jones?

to 400 on a piece of paper, how many times will you write the digit 3? 28. NO SLEEP

How many days can you go without sleeping?

29. ALPHABETIC ROBBERS

Alex, Ben and Chris were suspects in a bank robbery case. Alex testified that Ben was the robber. Ben testified that Chris was the robber. Chris said it was Ben. If two suspects

BOOK #

I CASES FROM THE OLD ATTIC 32. WITHOUT

What has roads without cars, rivers without water, mountains without forests?

33. THE BANDIT

Due to severity of the crime he had

committed, a bandit was sentenced to death. He could choose between three rooms. The first room was raging with fire, in the second room stood assassins with loaded guns and the third room was full of lions who hadn’t eaten in three years. Which room was the safest for the bandit?

35. METAL SHOES

In which sport does the main contestant wear shoes made completely out of metal? 36. WHEN THE FIRE STATION IS ON FIRE

What can you do when the fire station is on fire?

37. PANAMA HATS

Which country produces the

famous panama hats? Panama, Ecuador or Australia?

38. TRAVELLING TO AMERICA

Mimi travelled to America twice

with her husband Paul, and Paul only travelled to America once. How is this possible?

39. AT THE MORNING DEW HOTEL

At the luxury five-star Morning 34. IT STARTS WITH THE LETTER N

Mary’s father has four daughters: Nana, Nena, Nina and Nona. What is the name of the fifth daughter? Nuna?

BOOK #

Dew Hotel, the famous writer Nomiš Itamrađ ordered a cup of ginger tea. As he was about to take the first sip, he noticed a fly floating in the tea. He requested to speak to the manager, who apologised profusely, took the tea and, shortly afterwards, brought another cup of hot tea. However, Mr. Itamrađ noticed this

I CASES FROM THE OLD ATTIC was the same cup of tea that the manager had taken away. He sued the hotel and was compensated for the discomfort. The question is not how he won the lawsuit, but how he knew that the manager had served him the same tea. 40. THE NUMBER THAT FOLLOWS

Which number should be the next in line? 479 126, 47 926, 4 796, 796, __

41. CHICKENS IN THE YARD

Seven grey, five yellow and one

bill, tipped the waitress and left the restaurant. He was very careful once he stepped outside. The sky was black and the streets were empty. What happened? 44. BOILING EGGS

It takes ten minutes to cook a hardboiled egg, but boiling eggs is not always an easy task. Many factors can alter the time needed to boil an egg. For example, in some parts of the world, the time it takes to cook a hard-boiled egg can take up to 45 minutes. Why?

black chicken were in grandpa Al’s yard. How many chickens can say there is a chicken of the same colour?

42. A CLUMSY BURGLAR

During a break in, a burglar

knocked over a clock, which fell on the floor and stopped working. The next morning, the police weren’t able to determine the time of the break in. Why?

43. LUNCH AT THE RESTAURANT

Pete went to a restaurant and

ordered a sandwich and juice for lunch. After he finished, he paid the

45. HOME INVASION

Pete reported to the police that his home had been robbed the night before. “What was taken?”, asked the inspector. “As far as I know, not a thing,” answered Pete. How did Pete know his home was robbed?

BOOK #

I CASES FROM THE OLD ATTIC 46. THE CAB DRIVER AND THE COSTUMER

A man kept talking to a cab driver, who told him he was deaf and couldn’t hear him without his hearing device. The man stopped talking, but when they reached the destination, he realised that the cab driver had lied to him. How?

48. THE TALLEST MOUNTAIN

Which mountain was the tallest

before Mt. Everest was discovered?

49. RON AND HIS WIFE

How can Ron be behind his wife if she is in front of him?

50. A STRANGE POT 47. THE CAB DRIVER AND THE COSTUMER

BOOK #

You are holding a new, quality pot under the tap with running water, but it’s not filling up. Why? 51. A WORN TIRE

You have been travelling on an old dirt road covered with sharp rocks for over 150 kilometres with a worn tire. How is this possible?

II PROBLEMS FOR THE ROOKIE DETECTIVE

PROBLEMS FOR THE ROOKIE DETECTIVE

1. SCHOOL PAPER REPORTERS

Ike and Alex attended a math

competition in Norwich as school reporters. Lena, Ross and John all won prizes at this competition. Ike reported that Lena won first prize, while Ross was the runner-up. Alex, on the other hand, wrote that John won and that Lena was the runner-up. However, neither Ike nor Alex reported truthfully on the competition. Both stated one correct and one incorrect piece of information in their reports. Which prize was given to which competitor? 2. FAMILY REUNION

The following people attended the family reunion: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one

BOOK #

father-in-law, one mother-in-law and one sister-in-law. How many people were present at this reunion and who were they? 3. STATE COMPETITION

At the annual state-wide baseball

competition, 97 teams took part. This was a single-elimination tournament, in which 97 teams were split in pairs and each pair played a game. The losers were eliminated, while the remaining teams competed against each other, and so on. How many games were played until one team were the champions? 4. SOCKS IN A DRAWER

There are ten pairs of white and ten pairs of black socks in one of your drawers. If you take out only one sock without being able to tell its colour until its outside of the

PROBLEMS FOR THE ROOKIE DETECTIVE drawer, how many socks do you need to pull out in order to get a matching pair? 5. WINE CELLAR OWNER

Old man Abe, who owned a wine

cellar, bequeathed 21 barrels to his three sons. Seven were full with wine, seven were half-full, and seven were empty. The wine and the barrels had to be divided among his children so that each son got an equal number of full, half-full and empty barrels. They did not have anything that could help them measure the volume of wine in the barrels. How could the wine and the barrels be divided equally between the three brothers?

6. THE CAMEL RACE

Having reached old age, Abdul Aziz al-Sharaf, an Arab sheik, decided

to leave his fortune to his two sons – under one condition. His sons were to compete in a camel race and the second camel to cross the finish line would bring its owner immense wealth. For the next four days, the two brothers roamed aimlessly, as neither wanted to cross the finish line. Already desperate, they sought advice from a wise man called Musharraf. After he told them something, the two brothers quickly mounted the camels and bolted towards the finish line. What did the wise man Musharraf tell them? 7. JUGS

You have one 5-litre jug and one 3-litre jug. You have no other containers and there are no labels on the jugs. You need to fetch exactly seven litres of water from the river. How will you do this? Next, you will need only four litres of water. How will you achieve this? 8. PRIZE BEHIND THE DOOR

You are taking part in a TV contest

that hands out valuable prizes. There are three doors before you. The biggest prize is behind one of the doors. The host knows which doors lead to the prize. You are asked to

BOOK #

PROBLEMS FOR THE ROOKIE DETECTIVE pick one door and you oblige. Before you open it, the host opens one of the remaining doors and reveals there is no prize behind it, leaving you with one last chance to change your decision, if you wish to do so. Should you change your mind or does it make no difference? 9. ASKING THE RIGHT QUESTION

An old man was lost on his way to town. He got to the crossroads and didn’t know which road to take. Two men stood in the crossroads, with a sign next to them that said one man always spoke the truth and the other one always lied (without specifying which man did what). On the sign, it was also written that a traveller could only ask them one question. What did the old man ask to find out which road was the right one? 10. DONUTS WITH JAM

You have eight donuts with jam.

Seven donuts are equal in mass, while the eighth weighs more than the rest. You have a beam scale at your disposal. How many times do you have to measure the donuts before you can determine which one weighs the most?

BOOK #

11. THE BLUE LAGOON HOTEL

Three men were spending the night at the Blue Lagoon hotel. Max, the owner of the hotel, charged 30 dollars per night for a room. The men booked one room and each gave ten dollars. The bellboy took the tired guests to their rooms. Regretting he had overcharged his guests for the room, the owner told the bellboy to give them five dollars back. While climbing the stairs, the bellboy realized that five dollars couldn’t be divided into three equal parts, so he decided to keep two dollars and give the rest to the guests, a dollar each. This way, each guest paid nine dollars for the room, 27 dollars in total. The bellboy kept two dollars, which comes up to 29. Who had the 30th dollar?

PROBLEMS FOR THE ROOKIE DETECTIVE 12. THE COLOUR OF THE HAT

While on safari, Larry, Will and

Chris were captured by cannibals, who gave them one last chance to save themselves. They were tied to a stake so that Larry, who was in the back, could see the backs of two other men; Chris, who was in the middle, could see the back of the man in front of him; Will, the first one, could not see anyone. They were shown five hats, three were black and two were white. They were then blindfolded and one hat was put on each man’s head. The rest were hidden. The cannibals removed the blindfolds and told them they could all walk free if only one of them guessed the colour of the hat on his head. Time passed. Finally, Will – who couldn’t see anyone – correctly guessed the colour of the hat on his head. What colour was the hat and how did Will guess it?

13. LENA’S BIRTHDAY

Lena was celebrating her birthday. Two days later, her older twin brother Larry was celebrating his birthday. How is this possible?

14. AT THE PARTY

A married couple was throwing a party. They invited four more couples. During the party, the host asked the nine people who attended: “Out of all the people at this party, how many have you met before?” The host got nine different answers. How many people did the hostess know before the party? 15. THREE JUGS

You have three jugs. The first one holds 12 litres, the second one eight litres and the third one five litres. None of the jugs has a label denoting its capacity. The 12-litre jug is full, and the remaining two are empty. How will you divide 12 litres into two equal parts, so that two jugs contain exactly six litres each and third one remains empty? 16. RESULTS OF THE RACE

Mister Felix Figgins, horse racing

enthusiast and frequent visitor of the tracks, was about to place his bets as usual, but the bookmaker refused to tell him the outcome of the race. Instead, he posed a riddle on the top five places and told Mr. Figgins that he would cash out his bet only if he guessed the correct

BOOK #

PROBLEMS FOR THE ROOKIE DETECTIVE order in which the horses finished the race. This was the riddle: • Pearl finished in front of Belle and behind Whisper. • Whisper finished alongside Pearl, if and only if Lucky did not arrive at the same time as Jasper. • Pearl was behind Jasper by as many places as Jasper was behind Whisper, if and only if Whisper finished before Belle. Mr. Felix Figgins had a moment to think, then gave the correct answer. In which order did the horses finish the race? 17. FLOWERS

All of my flowers, except two, are roses. All of my flowers are tulips, except two. All of my flowers, except two, are carnations. How many flowers do I have?

BOOK #

18. THREE MEN AND THREE MONKEYS

After heavy tropical showers, three

men and three monkeys (one big and two small) were supposed to cross a flooded river. They only had one boat at their disposal, which could carry two bodies at a time, although only the men and the big monkey were strong enough to row. Moreover, the number of monkeys could never exceed the number of humans on the same side of the river, as they could attack people. How were they able to cross the river without anyone getting hurt? 19. THE CABLE

A computer cable has a plug with seven pins that form a perfect circle. The plug can be connected in seven different ways by turning it. The pins have been labelled with numbers from one to seven, so that each number was used only once. The same goes for the socket holes. The device that uses this cable requires that one pin on the plug corresponds to one hole in the socket. How should you mark the pins on the plug and the holes in the socket so that at least one of the pins matches the corresponding socket hole, regardless of how the cable is turned and plugged in?

9 788652 907410

LOGIC PUZZLES BOOK#3