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Overview
Product Details
| ISBN-13: | 9780906212776 |
|---|---|
| Publisher: | Tarquin Group |
| Publication date: | 09/01/1990 |
| Edition description: | None |
| Pages: | 76 |
| Product dimensions: | 5.83(w) x 5.71(h) x 0.30(d) |
| Age Range: | 10 - 16 Years |
Read an Excerpt
CHAPTER 1
The Two Families
The first set of logical puzzles introduces the members of both the Troo family and the Fals family, who have very different standards of behaviour. Members of the Troo family always tell the truth in every statement that they make and members of the Fals family always lie.
By looking at any person, you cannot tell which family he or she belongs to. The puzzle is to think about the statements that are made and then decide who is telling the truth and who is lying. From that you will be able to answer the question.
1 The first people you meet are Alan and Bert. Alan makes the following statement:
Alan: Both of us are from the Fals family. Which family does Alan belong to? What about Bert?
2 Next you meet Christine and Daphne. From Christine's statement, work out which family Daphne comes from.
Christine: Exactly one of us is from the Fals family.
3 The next two people you meet are Ernie and Fred. From what Ernie says, work out Fred's family.
Ernie: We are both from the same family.
4 Next you come across Gertrude and Hilda. Work out Hilda's family from Gertrude's statement.
Gertrude: Exactly one of us is from the Troo family. Is it possible to say which family Gertrude belongs to?
5 Now you find Ian and John. Ian makes the following statement:
Ian: At least one of us is from the Troo family. What can you say about Ian and John?
6 Karen and Laura are next. From Karen's statement can you say anything about the families they are from?
Karen: I am from the Fals family and Laura is from the Troo family.
7 Mark and Neil are the last people you meet. Mark makes the following statement:
Mark: It is not the case that Neil and I are both from the Troo family. Which families do Mark and Neil come from?
The solutions to THE TWO FAMILIES puzzles are on page 64.
CHAPTER 2More about the Families
In each of the first group of puzzles, only one person made a statement. In this second group, statements are made by two people and sometimes by as many as three. Since each person is a member of either the Troo family or the Fals family, each statement can be true or false. In each puzzle all the people may belong to the same or different families.
Since the names are not important, it seems simpler to refer to the people simply by capital letters, working consecutively through the alphabet.
1 You come across A and B. They make the following statements:
A: I belong to the Troo family.
B: We are both from the same family.
Which family do A and B belong to?
2 You next see C and D. Work out as much as you can about their families from the following statements:
C: We are from different families.
D: C is from the Fals family.
3 What can you say about the families of E and F from the following statements?
E: We are both from the Troo family.
F: E is not from the Fals family.
4 Next you see G and H who make the following statements:
G: I am from the Troo family.
H: G is from the Fals family.
What can you work out about these two?
5 The following two people you meet are I and J. They make the following statements:
I: We are from different families.
J: We are from the same family and I is lying.
Which families do I and J belong to?
6 Let us suppose that, when you met I and J in the previous puzzle, they made statements as follows:
I: We are from different families.
J: We are from the same family and I am lying.
Which families do I and J belong to this time? This puzzle may seem to be a repeat of the previous one, but look carefully at the changed wording.
7 K and L make the following statements:
K: It is not the case that I am from the Troo family and L is also from the Troo family.
L: K is from the Fals family.
What can you say about the families of these two?
8 Not surprisingly, the next two people you meet are called M and N. They say the following:
M: If I am from the Troo family than N is also from the Troo family.
N: We are both from the same family.
Which family does M belong to? What about N? Is N's statement necessary in solving the puzzle?
9 You next see O and P. They make the following statements:
O: Exactly one of these two statements is true.
P: Exactly one of these two statements is false.
Is it true that both O and P must come from the same family?
10 In the next four puzzles three people instead of just two are talking. Q, R and S say the following:
Q: R is from the Fals family.
R: S is from the Troo family.
S: Either I am from the Fals family or I am from the Troo family.
Which families are the three from?
11 T, U and V are next. From their statements, can you work out the families that they are from?
T: U is a different family from V.
U: V is from the Fals family.
V: At least one of us is from the Fals family.
12 You see W, X and Y. They say the following:
W: X is from the Fals family.
X: We are all from the same family.
Y: At least one of us is from the Fals family.
Which one comes from which family?
13 ZA and ZB have double initials, but they are still from the same families as Z and the others. They make these statements:
Z: At least one of us is from the Troo family.
ZA: That's a lie!
ZB: If ZA said "That is true" then you couldn't work out which family he belonged to.
When solving this puzzle you must assume that ZA was referring to Z's statement when he said "That's a lie!" This puzzle is quite difficult to solve.
14 This is another quite difficult puzzle. From these statements made by ZC, ZD and ZE, can you work out which families that they came from (if it is possible)?
ZC: ZD and ZE belong to the same family.
ZD: ZC and ZE belong to the same family.
ZE: I do not belong to the same family as ZD.
The remaining four puzzles in this chapter are also about 3 members of the two families but only the first two will make statements. You have to work out the families that the silent third person comes from using the statements of the other two people.
15 ZF and ZG make the following statements about themselves and ZH:
ZF: Exactly one of the three of us is from the Fals family.
ZG: ZI and ZK are from different families.
Which family is ZH from?
16 From the two statements made by ZI and ZJ, can you work out which family that ZK is from?
ZI: ZJ is from the Troo family.
ZJ: ZI and ZK are from different families.
17 ZL, ZM and ZN are next. ZL and ZM say the following:
ZL: ZM is from the Fals family.
ZM: ZL and ZN are from the same family.
Again, this puzzle is similar to the previous one. I have changed the word "Troo" to "Fals" in ZL's statement and "different" to "the same" in ZM's statement. Which family is ZN from?
18 ZO and ZP say the following about themselves and ZQ:
ZO: All three of us are from the Troo family.
ZP: All three of us are from the Fals family.
Which family is ZQ from? With so little information, can you also say which families ZO and ZP are from?
The solutions to MORE ABOUT THE FAMILIES start on page 64
CHAPTER 3Classes 1, 2 and 3
The puzzles in this group all concern the members of three classes in a certain school. Members of class 1 always tell the truth, so every statement they make is true. Members of class 2 always lie, so every statement is false. Members of class 3 can tell the truth or lie as they prefer at the time.
For each puzzle one person from each class is present. Everyone in the school knows who belongs to each class, but other people cannot tell them apart except by thinking about what they say. To solve the puzzle you have first to decide who is telling the truth and who is lying. Hopefully it is then just a short step to answering the question.
1 You meet A, B and C. They say the following:
A: Of these three statements, exactly two are true.
B: If I am from class 2 then A is from class 3.
C: I am not from class 1.
Which classes are A, B and C from?
2 D, E and F are next. From their statements, work out which classes they are from:
D: E is from class 3.
E: D is from class 1.
F: I am from class 3.
3 G, H and I make the following statements
G: I am from class 2.
H: I am from class 3.
I: G is from class 3.
Which classes are they from?
4 J, K and L are next. They say the following:
J: I am not from class 3.
K: J is not from class 3.
L: J's statement has the same truth value as K's statement.
Which classes are the three from? You must know that, when L said "has the same truth value as" he meant that J's statement and K's statement are both false or both true.
5 The next three people to make statements are M, N and O. Which classes are they from?
M: Of myself and N, just one of us is from class 2.
N: O is from class 1.
O: M is from class 2.
6 P, Q and R are next. They make the following statements: P: Q is from class 3 and I am from class 2.
Q: P is from class 1 and R is from class 3.
R: I am from class 1.
I do not ask you to find out which class each person is from because this puzzle would not be possible. However, you can find out which class R is from and whether Q's statement is true or false.
7 S, T and U say the following: S: T is from class 3.
T: I am from class 3.
U: I am from class 3.
Who is a member of which class?
8 Suppose S, T and U had said the following:
S: T is from class 3.
T: I am from class 3.
U: I am not from class 3.
This puzzle is very similar to the previous one. The only difference is in U's statement but that is sufficient to change the answer completely.
9 V, W and X are the last three. They each make statements as follows:
V: I am from class 1.
W: I am from class 2.
X: I am from class 3.
This puzzle is quite easy but it often catches people out. What class is each person from?
The solutions to the CLASSES 1, 2 AND 3 puzzles are on page 66.
CHAPTER 4Whose Room is it?
In this group of puzzles the Troo and Fals families all went to a holiday village on a small island. Each adult had his or her room, which was numbered, but because the two families were friends, they spent a lot of time visiting each other.
I went on holiday to the same village and thought it would be interesting to find out the room number of everyone. The Troos always tell the truth, but the members of the Fals family still always lie. All of them know which family everyone comes from, but I could not tell them apart except by thinking about what they said.
Two or three people were present in each room that I visited, always including the owner. The puzzle is to find out from their statements who is telling the truth and who is lying. Once that is established, it should be a simple matter to determine which room it was and which family he or she belonged to.
There is also an interesting puzzle about their room numbers.
1 The first room I went to was number 2. A and B were there. They said the following:
A: Both of us are from the Fals family.
B: I occupy this room.
Whose room is it? Is it the occupier of the Troos or the Fals family?
2 C and D are in the second room. They made the following statements:
C: Exactly one of us is from the Troo family.
D: C is staying in this room.
Whose room number is it and is she telling the truth? This time the room number was number 16.
3 I went next to number 29. E and F were there and said the following:
E: At least one of us is from the Troo family and this is my room.
F: Both of us are from the Fals family and it is my room.
Whose room is it? Can you work out which family the owner is from?
4 The next room was number 4. The two people in there, G and H, said the following:
G: At least one of us from the Fals family and H is staying in this room.
H: G is from the Troo family.
Whose room is it and which family is the occupant from?
5 The next room I visited was room number 17. I and J were there and made the following statements:
I: We are either both from the Fals family or both from the Troo family.
J: This room is mine.
Is it really J's room? Is he telling the truth?
6 K, L and M were in the next room which was number 7. They said the following:
K: This is my room.
L: This is my room.
M: I am from the same family as L.
K and L cannot be telling the truth! Whose room is number 7 and which family is the occupant from?
7 The final room that I visited was number 15. N, O and P were there. They each made a statement:
N: This room belongs to P.
O: I am from the same family as P.
P: The room belongs to N. Whose room is it and which family is he or she from?
Is it possible that I and P are brother and sister?
8 I was about to visit room 11 when I realised that there was a pattern to the answers so far. Simply by looking at the room number I was able to tell whether the occupant was a Troo or a Fals. What was the rule and what family did the occupant of room 11 belong to?
There were 30 rooms in the holiday village, numbered from 1 to 30. I was staying in room 1 and the other 29 rooms were all occupied by the Troo or Fals families. How many of each were there?
The solutions to the WHOSE ROOM IS IT? puzzles are on page 67.
CHAPTER 5Who does it Belong to?
This group of puzzles brings us back to the pupils of classes 1, 2 and 3 who are now arguing over various objects which have been found in the school. The pupils of class 1 still always tell the truth as before. The pupils of class 2 always lie and the pupils of class 3 sometimes lie and sometimes tell the truth. One person from each class is present in each discussion.
The additional piece of information is that the owner of the object always lies. However, in spite of this extra difficulty it is still possible to find out who does own it. That is the puzzle.
1 A, B and C are talking about a ruler. They say the following:
A: This ruler belongs to me.
B: A is lying.
C: Of these three statements, exactly two are true.
Who owns the ruler?
2 D, E and F make the following the statements:
D: The football belongs to me.
E: D is from class 1.
F: The football belongs to E.
Who owns the football?
3 G, H and I are talking about a pencil. Who owns it?
G: I own the pencil.
H: Exactly one of these three statements is false.
I: H is from class 2.
4 J, K and L are talking about an apple. From their statements, can you work out who owns it?
J: The apple belongs to L.
K: J is from class 1.
L: J's statement is false.
5 M, N and O say the following:
M: The book belongs to O.
N: The book belongs to O.
O: The book is not mine.
Who owns the book? You are not able to solve this puzzle with that information only so I will tell you that more people are telling the truth than are lying. Now it is really easy.
6 P, Q and R are talking about a lunch box. Whose it is?
P: At least one of these three statements is false.
Q: The lunch box belongs to P.
R: The lunch box does not belong to P.
The solutions to the WHO DOES IT BELONG TO? puzzles are on page 68.
CHAPTER 6The Tals and the Froos
The well-known families of the Troos and the Fals began to intermarry and to have children. These children shared the characteristics of their parents as other children do. It was found that when a Troo man married a Fals woman, their sons always told the truth and their daughters always lied. When a Fals man married a Troo woman it was the daughters who told the truth and the sons who lied.
Usually a family takes its surname from the father, but that would cause problems in these families. Females from a family with a Troo father would carry the name Troo until they married but would tell lies. Likewise boys with the surname Fals would tell the truth. This would be most confusing. The answer was to use the surname TALS for the children with a Troo father and FROO for children with a Fals father. Hence Tals males and Froo females always tell the truth and Tals females and Froo males always lie.
Now for the puzzles!
1 The first speaker, A, says the following:
A: I am a Froo male.
Is A male or female and which family does he or she come from?
2 B, the second person, says the following:
B: I am a Tals female.
What can you say about B?
3 C is third. C makes the following statement:
C: I am not a Tals male.
Which family does C come from? Is C male or female.
4 From the simple statement below, work out as much about D as you can.
D: I am from the Tals family.
5 E says the following:
E: I am female.
What can you say about E?
6 F makes the following statement:
F: I am from the Froo family.
What can you say about F?
7 G is next and says the following:
G: I am male.
Do you really need to work this out? What can you say about G?
(Continues…)
Excerpted from "Who Tells the Truth?"
by .
Copyright © 2006 Adam Case.
Excerpted by permission of Tarquin Publications.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
Table of Contents
The Two Families,
More about the Families,
Paradoxical Pictures,
Classes 1, 2 and 3,
Whose Room is it?,
Who does it Belong to?,
Paradoxical Pictures,
The Tals and the Froos,
John and his Twins,
Talking to the Tals and Froos,
Who is Holding the Card,
The Farewell Party,
Hints and Solutions,