Hey, this is Presh Talwalkar and you're watching Mind Your Decisions.
Here's a fun logic test.
Which answer in this list is the correct answer to this question?
Number one: all of the below.
Number two: none of the below.
Number three: all of the above.
Number four: one of the above.
Number five: none of the above.
Number six: none of the above.
I saw this problem on Math Stack Exchange,
And I'll mention my videos will make you so smart that problems like this will start to seem easy.
But math is about constant training. Just as marathon runners practice with 5k runs,
People who solve the world's hardest problems practice with easier ones. Don't let the math meanies tell you otherwise.
In this videos' "you feature me, I feature you,"
I want to mention Mental Floss featured one of my logic puzzles: "Can you guess the secret word in this brain teaser?"
Check out the Mental Floss article and check out my video.
So, can you figure out this problem?
Give it a try, and when you're ready, keep watching the video for a solution.
So, how can we solve this logic problem? We'll start out by evaluating each of the statements.
First consider statement 1: all of the below.
If statement 1 is true that implies all of the statements below, including 5, are true.
But if statement 5 is true, that means none of the statements above 5 can be true, including statement 1.
That would imply statement 1 has to be false.
This means 1 is a self contradicting statement and cannot be true.
So we'll mark that statement 1 cannot be true.
Now, let's skip statement 2 for a second and consider 3: all of the above.
If 3 is true that implies 1 is true.
But we already concluded 1 is self-contradictory and cannot be true.
This means 3 also cannot be true
Now, let's go to statement 2: none of the below.
if statement 2 is true that implies statement 4 has to be false.
4 Says that one of the above is true.
So if 4 is false, that means none of the above can be true.
So if 4 is false, since one and three are already known to be false, we must have that two is false.
Hence we have that 2 is a self contradictory statement and also cannot be true.
Now, consider statement 4.
If 4 is true, then 1, 2, or 3 has to be true.
But we already concluded that 1, 2, & 3 cannot be true. This means statement 4 has to be false.
Now let's skip statement 5 for a second and go to statement 6: none of the above.
If 6 is true, then 5 has to be false.
Implying some statement 1, 2, 3, or 4 has to be true.
But we already know 1, 2, 3, & 4 are false so statement 6 cannot be a true statement.
So now we're left with statement 5: none of the above. Can 5 be true?
Yes it can!
If 5 is true, we would need 1, 2, 3, & 4 to be false, which we already worked out.
So there's no contradiction if we have that 5 is a true statement.
So the correct answer is 5.
Did you figure it out?
Thanks for watching this video.
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