True or False Statements (Gardner)

  • Thread starter MrJones
  • Start date
  • #1
8
0
This is the sort of teaser that appears in a book written by Martin Gardner, and I was hoping someone could help me see my way to the answer.

Of the following six statements, which are true and which are false?

1. There are no false statements in this card.
2. There is exactly one false statement in this card.
3. There are exactly two false statements in this card.
4. There are exactly three false statements in this card.
5. There are exactly four false statements in this card.
6. There are exactly five false statements in this card


I feel like I must be overanalyzing this one
 

Answers and Replies

  • #2
drizzle
Gold Member
366
57
.....Where is this card?
 
  • #3
D H
Staff Emeritus
Science Advisor
Insights Author
15,393
685
.....Where is this card?
I assume the OP meant this set. Don't overanalyze.

Each statement makes an exact claim that is contrary to the exact claims made by the other statements. Thusly, there cannot be two or more true statements, which in turn means at least five of the statements must be false.

1. Assume exactly five statements are false. This is statement six. Statement six is true and the others are false.

2. Assume all six statements are false. This is also consistent.


Bottom line: Statements 1-5 are false, the veracity of statement 6 cannot be determined.
 
  • #4
180
1
This is the sort of teaser that appears in a book written by Martin Gardner, and I was hoping someone could help me see my way to the answer.

Of the following six statements, which are true and which are false?

1. There are no false statements in this card.
2. There is exactly one false statement in this card.
3. There are exactly two false statements in this card.
4. There are exactly three false statements in this card.
5. There are exactly four false statements in this card.
6. There are exactly five false statements in this card


I feel like I must be overanalyzing this one
6. The previous 5 statements are falese, which is true. It's the only true answer.
 
  • #5
D H
Staff Emeritus
Science Advisor
Insights Author
15,393
685
The only thing that can be said with certainty is that statements 1-5 must be false. The last statement can be either true or false and still be consistent. It's truth value is indeterminate.
 
  • #6
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
12,116
152
6. The previous 5 statements are falese, which is true. It's the only true answer.
But #6 doesn't say there are at least 5 false statements, it says there are exactly 5 false statements.

D H is correct, #6 could be either true or false.

This reminds me of a question I heard on the TV show Whose Line Is It Anyway (American version):

Multiple choice: the correct answer is
A. B
B. C
C. A
D. D​
 
  • #7
DaveC426913
Gold Member
18,934
2,429
Multiple choice: the correct answer is
A. B
B. C
C. A
D. D​
:rofl:
 
  • #8
180
1
But #6 doesn't say there are at least 5 false statements, it says there are exactly 5 false statements.

D H is correct, #6 could be either true or false.
Let's review the initial problem:

"Of the following six statements, which are true and which are false?"

And the sixth question:

"6. There are exactly five false statements in this card"

The initial problem provides no option for indeterminancy. Therefore, it must either be true, or must either be false. "...could be either true or false" is not an option.

#6 is the only statement which can be true. Since it must be either true or false, the choice is up to the reader. I choose that it's ture. :wink:
 

Related Threads on True or False Statements (Gardner)

  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
13
Views
9K
  • Last Post
2
Replies
35
Views
10K
  • Last Post
Replies
3
Views
7K
  • Last Post
Replies
13
Views
14K
Replies
7
Views
1K
Replies
10
Views
4K
  • Last Post
2
Replies
27
Views
4K
Replies
42
Views
8K
Replies
8
Views
3K
Top