The Riddle Answers

Okay, so I posted some riddles and paradoxes on Thursday, and here are the answers!

The sentence below is true.
The sentence above is false.
(which sentence is true, which is false?)
This is a paradox :)

What is the probability of getting this question correct?
a) 25% b)50% c)75% d)25%
Okay, so this is a trick question haha. I believe when all calculated out, the answer is 13 out of 36, or 36.1%. This is because there are two 25%, so there is a 1/3 chance of choosing a 25%. Then, out of that 1/3, there's a 1/2 chance of choosing the correct 25%. So the average is 5/12. And then for the other two, 50% and 75%, there is a combined 2/3 chance of choosing them. Average 5/12 and 2/3, and you get 13/36

Monty Hall RiddleThere are three doors. Behind one is money, and the other two doors have nothing behind them. You want to pick the door with money, quite obviously. You choose one door. Of the other two doors, a man, Monty Hall, opens one empty door. You are then offered the choice of staying with your original door, or switching to the other door. Should you stay, switch, or does it not matter either way?
The answer is, you should switch. There are three scenarios:
--You've chosen the door with money. Monty Hall reveals an empty door. If you switch, you lose.
--You've chosen one of the empty doors. Monty Hall reveals an empty door. If you switch, you win.
--You've chosen the other empty door. Monty Hall reveals an empty door. If you switch, you win.
Switching gives a 2/3 chance of winning! :)

Pop Quiz RiddleA teacher tells his class, "I will be giving a pop quiz some day next week, and I guarantee you will not know the quiz is happening until you come into class that day."
Gina, one of the students in the class, thinks about the teacher's statement and determines that the quiz could not possibly be on Friday, because if it were, then all of the students would know this on Thursday night, which would would contradict what the teacher said about the quiz being a surprise.
She then determines the quiz could not be on Thursday either, because if it was, all the students would know by Wednesday night (since the quiz hadn't yet happened, and thus must be on Thursday or Friday, but since we already determined it couldn't be on Friday, it must be Thursday). Again, this wouldn't be a surprise, contradiciting what the teacher said, and so the quiz couldn't be on Thursday.
Using the same logic, she then determines that the quiz could not be on Wednesday, or Tuesday, or Monday. Thinking that the teacher must have been contradicting himself, Gina decides that no matter what day the quiz is, she will always know.
Much to Gina's surprise, the teacher announces on Tuesday that he is giving a pop quiz. Gina is surprised, just as the teacher said she would be.
What was wrong with Gina's reasoning?
Okay....so there's actually no specific answer, as the riddle is still being debated. Here are a two possible solutions:
--Gina is not allowed to eliminate Thursday on Tuesday night, as she hasn't had the Wednesday lesson yet, ergo her logic is incorrect after she eliminates Friday.
--Although Gina has eliminated all the days, she still has no idea what day the quiz will be, so she will still be surprised.

Liar and a Truth-teller (easiest version)You are walking down a path when you come to a fork in the road. One road leads to the Truth Village where everyone tells the truth. One road leads to the Lie Village where everyone lies. You want to go to the Truth Village, but don't know which road to take. (oh, and for some odd reason if you take the wrong path you can't turn back LOL)
In front of the doors are two twin brothers, one from each village. One of the brothers always lies, and the other always tells the truth. You don't know which brother is the liar and which is the truth-teller.
You are allowed to ask one single question to one of the brothers (not both) to figure out which door to open.
What question should you ask?
You should ask: "Which village do you come from?" The truth teller will point to the truth village, and the liar will also point to the truth village.

Liar and a Truth-teller (slightly harder version)You are walking down a path when you come to a fork in the road. One road leads to the Truth Village where everyone tells the truth. One road leads to the Lie Village where everyone lies. You want to go to the Truth Village, but don't know which road to take. (again, you can't turn back if you choose the wrong road...)
In front of the doors are two twin brothers that know which village is which, but do not actually come from the villages themselves. One of the brothers always lies, and the other always tells the truth. You don't know which brother is the liar and which is the truth-teller.
You are allowed to ask one single question to one of the brothers (not both) to figure out which door to open.
What question should you ask?
You should ask: "What would the person next to you say if I asked which way the lie village was?" This way, the truth teller will point to the truth village. The liar will also point to the truth village. (you can also ask "what would the person next to you say if I asked which way the lie village was?" in which case they both would point to the lie village haha)

Liar or a Truth-teller (hardest version)You're walking down a path and come to two doors. One of the doors leads to a life of prosperity and happiness, and the other door leads to a life of misery and sorrow. You don't know which door is which.
In front of the door is ONE man. You know that this man either always lies, or always tells the truth, but you don't know which. The man knows which door is which.
You are allowed to ask the man ONE yes-or-no question to figure out which door to go through. To make things more difficult, the man is very self-centered, so you are only allowed to ask him a question about what he thinks or knows; your question cannot involve what any other person or object (real or hypothetical) might say.
What question should you ask to ensure you go through the good door?
You should ask: "Is the good door on the left?" (or right. you could also ask about the wrong door). There are four scenarios:
--truth teller, you've pointed at the right door: will say yes
--liar, you've pointed at the right door: will say yes
--truth teller, you've pointed at the wrong door: will say no
--liar, you've pointed at the wrong door: will say no

Three people check into a hotel room. The bill is $30 so they each pay $10. After they go to the room, the hotel's cashier realizes that the bill should have only been $25. So he gives $5 to the bellhop and tells him to return the money to the guests. The bellhop notices that $5 can't be split evenly between the three guests, so he keeps $2 for himself and then gives the other $3 to the guests.
Now the guests, with their dollars back, have each paid $9 for a total of $27. And the bellhop has pocketed $2. So there is $27 + $2 = $29 accounted for. But the guests originally paid $30. What happened to the other dollar?
Actually, it makes no sense to add the 2 to the 27, because the $27 that has been paid includes the $2 the bellhop made.
The correct math is to say that the guests paid $27, and the bellhop took $2, which, if given back to the guests, would bring them to their correct payment of $27 - $2 = $25.

Jenny was 17 the day before yesterday. Next year she will turn 20. How is this possible?
Today is January 1. The day before yesterday was December 30, and Jenny was 17. On December 31, Jenny turned 18. This year on Dec. 31, Jenny will turn 19. Next year, on Dec.31, Jenny will turn 20!

Okay, so that's all! :) I'm not much of an explainer, so tell me if this didn't make sense.

--Audrey