# Possible explanation for a question

Hello, I solved a little question in the "Joy of Problem Solving" course and I want to share with you another possible explanation for this question:

Suppose that the local is a knave, so his answer "Yes." means no (he is a knave so he's a liar). Therefore, the statement "If you are a liar , then 1+1 = 2" should be false (if he's really a knave). The statement will only be false only if the hypothesis is true ("If you are a liar") and the conclusion is false ("1+1 =2"). This statement can't be false because the conclusion is true (1+1 really equals to 2). That means that this case is not possible and the man is not a knave, but a knight.

Do you think this is a better explanation?

Note by Idan D
11 months, 1 week ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

Good point. I've updated the solution to reflect this. Thank you for your input.

Staff - 11 months, 1 week ago

There seems to be extra space in the quotation rows

- 11 months, 1 week ago

Hi Mahdi, I can't seem to find the extra space that you're referencing.

Staff - 11 months ago

- 11 months ago

Here you go, under the first and the second quotes, each has an extra empty line. Not much of a big deal though!

- 11 months ago

Wow, good eye! Thank you, let me file a bug report.

Staff - 11 months ago

No worries, that is not a big deal at all! Most people wouldn't even notice, but it just feels great when everything controllable is perfect :)

- 11 months ago

Keep up the good work Mahdi!

Staff - 11 months ago