MATHS QUIZ 7 LOGIC NO. 2

[magpie in the 80's]

9. Statement 2 is true

incorrect diss

[magpie in the 80's]

7. Yes.

Man 2 would always say Man 1.
Man 1 (the liar) would say either;

- Man 2 (and then Man 3 would say Man 3 to be different)
- Man 3 (and then Man 3 would say Man 1 to be different)

(unless I've totally misread that)

incorrect diss

[magpie in the 80's]

I'd give you more of a hand Psuedo but time isn't allowing me today!

Anyway, Qu 8 I think Statement C is false

I reckon it's B.

We got a nerd-off situation! Adjudication please Mitty!

the answer is B
correct pseudo

[magpie in the 80's]

6. Just statement 3 is true?

If just 3 was true, then the sum of false statements would be 3, meaning 2 would have to be true also.

I reckon none of 'em is true.

correct again pseudo

[magpie in the 80's]

4

A false
B false
C true
D true

correct c and d are telling the truth
well done again professor pseudo

[magpie in the 80's]

just Q5 Q7 and Q9 to go

[Pseudo]

5. Which of the following statement(s) is/are true?

Statement A: There are exactly three false statements
Statement B: There is exactly one false statement
Statement C: There are exactly two true statements
Statement D: There are exactly four true statements

This could be rewritten:

A: There is exactly one true statement
B: There are 3 exactly true statements
C: There are 2 exactly true statements
D: There are 4 exactly true statements

All of which are mutually exclusive; i.e. at most one could be true. B, C and D are therefore all false. A could be either true or false.

7. Man 1 is a liar, man 2 is a truth teller, and man 3 is contradictory. If you asked each one of them, "who is the liar?" would there be a sure chance that all three of them answer differently?

I read this the same way as Diss, and would have given the same answer.

9.
Statement 1: The sum of the true statements, is 3
Statement 2: The sum of the false statements, is 1

Equivalent to the following -
statement 1: 1 and 2 are true
statement 2: 1 is false and 2 is true

if 1 is true, then 2 is true, then 1 is false => contradiction => 1 is false
statement 2 then reduces to "this statement is true" and could be true or false.

[magpie in the 80's]

5. Which of the following statement(s) is/are true?

Statement A: There are exactly three false statements
Statement B: There is exactly one false statement
Statement C: There are exactly two true statements
Statement D: There are exactly four true statements

This could be rewritten:

A: There is exactly one true statement
B: There are 3 exactly true statements
C: There are 2 exactly true statements
D: There are 4 exactly true statements

All of which are mutually exclusive; i.e. at most one could be true. B, C and D are therefore all false. A could be either true or false.
A IS THE CORRECT ANSWER............... We know statement D is false because if it is true, then all four statements have to be true, which is impossible if statements B & C claim that there are false statements. Statement D is false.
Statement B cannot be true, because if it is, then statements A & C have to be true also, since statement D is false. This is contradictory, so statement B is false too.
Statement C is false too, because if it is true, then statement A would have to be true too, which is also contradictive.
Statements B, C, & D are false, so if there are three false statements, then statement A is true. Nothing is contradictive here.

7. Man 1 is a liar, man 2 is a truth teller, and man 3 is contradictory. If you asked each one of them, "who is the liar?" would there be a sure chance that all three of them answer differently?

I read this the same way as Diss, and would have given the same answer.
CORRECT ANSWER IS NO....... Man 3 would say, "I am the liar," man 2 would say "man 1 is the liar," but man 1 would say either, "man 2 is the liar," or "man 3 is the liar." You cannot be sure to get distinct answers from all three of them.

9.
Statement 1: The sum of the true statements, is 3
Statement 2: The sum of the false statements, is 1

Equivalent to the following -
statement 1: 1 and 2 are true
statement 2: 1 is false and 2 is true

if 1 is true, then 2 is true, then 1 is false => contradiction => 1 is false
statement 2 then reduces to "this statement is true" and could be true or false.
CORRECT ANSWER IS ...CANNOT BE FIGURED OUT............ If statement 1 is true, then statement 2 has to be true in order for the sum to be 3. In order for statement 2 to be true, statement 1 has to be false. Statement 1 must be false in order for it to be true. This is not possible, so statement 1 is false. So far, the sum of the false statements is 1. This is exactly what statement 2 said, so most people would think statement 2 is true, and statement 1 is false. If you further examine this, statement 2 can be false as well. If both statements are false, then the sum of the false statements is not 1, and the sum of the true statements is not 3. Everything still works out when statement 2 is false, therefore, this question cannot be figured out.

[magpie in the 80's]

1. You want to join a logician club, but you can only join if you figure out where the clubhouse is located. If two of these statements are true, and two are false, where is the clubhouse located?

The clubhouse is on Kayton Street
The clubhouse is on Firal Street
The clubhouse is not on Firal Street
The clubhouse is not on Vilo Street
THE CLUBHOUSE IS ON FIRAL STREET
2. You are on a game show. You must decide which boxes the gold can be in. You have two tries, which two boxes should you pick? There can be any number of true or false statements.

Box A: The gold is in box C
Box B: The gold is in box A
Box C: Two statements are true
Box D: The box the gold is in is lying

BOX B AND BOX C
3. If you earn twice as much as one more dollar as you earned the previous day, how much money did you earn on June 25, if you earned 12 dollars on June 27?
$1.50

4. Which of the following statement(s) is/are true?

Statement A: There is one true statement in this question
Statement B: Statement A is telling the truth
Statement C: Statement B is lying
Statement D: This statement is true
C AND D

5. Which of the following statement(s) is/are true?

Statement A: There are exactly three false statements
Statement B: There is exactly one false statement
Statement C: There are exactly two true statements
Statement D: There are exactly four true statements
STATEMENT A

6. Which statement(s) is/are true?

Statement 1: The addition of the true statements equals 5.
Statement 2: The addition of the false statements equals 3.
Statement 3: The addition of the true statements equals 3
NONE ARE TRUE

7. Man 1 is a liar, man 2 is a truth teller, and man 3 is contradictory. If you asked each one of them, "who is the liar?" would there be a sure chance that all three of them answer differently?
NO


8. Which statement is false if only one is false?

Statement A: Statement D is true
Statement B: Statement A is false
Statement C: Statement B is false
Statement D: Statement C is true
STATEMENT B

9. Which of the following statements are true?

Statement 1: The sum of the true statements, is 3
Statement 2: The sum of the false statements, is 1
CANNOT BE FIGURED OUT


10. There are four boxes lined up on a desk from left to right. Which box is the gold in if the two truthful boxes are not next to each other, and the two lying boxes are not next to each other?

Box A: The gold is not in this box
Box B: The gold is in this box
Box C: The gold is in this box
Box D: The gold is in this box
THE GOLD IS IN BOX C

QUESTIONS ANSWERED ARE IN RED.
QUESTIONS UNANSWERED ARE IN BLUE.

END OF QUIZ

[Dissident]

I read this the same way as Diss, and would have given the same answer.
CORRECT ANSWER IS NO....... Man 3 would say, "I am the liar," man 2 would say "man 1 is the liar," but man 1 would say either, "man 2 is the liar," or "man 3 is the liar." You cannot be sure to get distinct answers from all three of them.

I was assuming they would be asked in order.
Or something like that.

Or at least the "contradictory" man would be asked last.