Can You Solve This Tricky Multiple Choice Question?

Hi,

this

is Presh Talwalkar and you are watching Mind Your Decisions. Here is a fun logic puzzle. Which answer on

this

list is the correct answer to

this

question

? Number one: all of the following. Number two: none of the following. 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 the Math Stack Exchange, and I'll mention that my videos will make it so smart that problems like

this

will start to look easy. But mathematics is about constant training.

Just as marathon runners practice with 5k races, the people who

solve

the world's hardest problems practice with the easiest. Don't let the bad mathematicians tell you otherwise. In

this

"you introduce me, I introduce you" video, I want to mention that Mental Floss introduced one of my logic puzzles: "Can you guess the secret word in

this

puzzle?" Check out the Mental Floss article and watch my video. So can you

solve

this

problem? Give it a try, and when you're ready, keep watching the video to find a solution. So how can we

solve

this

logic problem? We will begin by evaluating each of the statements.

First consider statement 1: all of the following. If statement 1 is true, that implies that all the statements below, including 5, are true. But if statement 5 is true, that means that none of the statements before statement 5 can be true, including statement 1. That would imply that statement 1 has to be false.

This

means that 1 is a statement that contradicts itself and cannot be true. So we will mark that statement 1 cannot be true. Now, let's skip statement 2 for a second and consider statement 3: all of the above. If 3 is true, that implies that 1 is true. But we already conclude that 1 is self-contradictory and cannot be true.

This

means that 3 cannot be true either. Now, let's go to statement 2: none of the following. if statement 2 is true, that implies that 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 two to be false. Therefore, we have that 2 is a self-contradictory statement and cannot be true either. Now consider statement 4. If 4 is true, then either 1, 2, or 3 must be true. But we already concluded that 1, 2 and 3 cannot be true.

This

means that 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 must be false. Implying some statement 1, 2, 3 or 4 has to be true. But we already know that 1, 2, 3, and 4 are false, so statement 6 cannot be a true statement. So now we are left with statement 5: none of the above. 5 can be true? Yes it can! If 5 is true, we would need 1, 2, 3, and 4 to be false, which we already figured out. Then there is no contradiction if we have that 5 is a true statement. So the correct answer is 5.

Did you find out? Thanks for watching

this

video. These math videos inspire and build confidence for people around the world and already have over 100 million views. But evil mathematicians unfairly criticize them and spread their negativity. Let's be extra positive to cancel them. Please help us by subscribing for free to get the latest videos and by watching and sharing all Mind Your Decisions videos. You can email me with a brain teaser or math topic: presh mindyourdecisions com If you like, you can also check out my books that are linked in the video description, and you can support me on Patreon for exclusive rewards.

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