You have two jugs, one that holds exactly 3 gallons, and one that holds exactly 5 gallons. Using just these two jugs and a fire hose, how can you measure out exactly 4 gallons of water?
Fill the 5-gallon jug to the top, and then pour it into the 3-gallon jug until the 3-gallon jug is full. You now have 2 gallons remaining in the 5-gallon jug. Pour out the 3-gallon jug, and then pour the 2 gallons from the 5-gallon jug into the 3-gallon jug. Finally, fill the 5-gallon jug to the top and pour it into the 3-gallon jug until it's full. Since there was only space left for 1 more gallon in the 3-gallon jug, you now have exactly 4 gallons in the 5-gallon jug.
You've been placed on a course of expensive medication in which you are to take one tablet of Plusin and one tablet of Minusin daily. You must be careful that you take just one of each because taking more of either can have serious side effects. Taking Plusin without taking Minusin, or vice versa, can also be very serious, because they must be taken together in order to be effective. In summary, you must take exactly one of the Plusin pills and one of the Minusin pills at one time.
Therefore, you open up the Plusin bottle, and you tap one Plusin pill into your hand. You put that bottle aside and you open the Minusin bottle. You do the same, but by mistake, two Minusins fall into your hand with the Plusin pill.
Now, here's the problem. You weren't watching your hand as the pills fell into it, so you can't tell the Plusin pill apart from the two Minusin pills. The pills look identical. They are both the same size, same weight (10 micrograms), same color (Blue), same shape (perfect square), same everything, and they are not marked differently in any way.
What are you going to do?
You cannot tell which pill is which, and they cost $500 a piece, so you cannot afford to throw them away and start over again. How do you get your daily dose of exactly one Plusin and exactly one Minusin without wasting any of the pills?
Carefully cut each of the three pills in half, and carefully separate them into two piles, with half of each pill in each pile. You do not know which pill is which, but you are 100% sure that each of the two piles now contains two halves of Minusin and half of Plusin. Now go back into the Plusin bottle, take out a pill, cut it in half, and add one half to each stack. Now you have two stacks, each one containing two halves of Plusin and two halves of Minusin. Take one stack of pills today, and save the second stack for tomorrow.
After recent events, Question Mark is annoyed with his brother, Skid Mark. Skid thought it would be funny to hide Question's wallet. He told Question that he would get it back if he finds it. So, first off, Skid laid five colored keys in a row. One of them is a key to a room where Skid is hiding Question's wallet. Using the clues, can you determine the order of the keys and which is the right key?
Red: This key is somewhere to the left of the key to the door.
Blue: This key is not at one of the ends.
Green: This key is three spaces away from the key to the door (2 between).
Yellow: This key is next to the key to the door.
Orange: This key is in the middle.
The order (from left to right) is Green, Red, Orange, Blue, Yellow. The blue key is the key to the door.
A monk leaves at sunrise and walks on a path from the front door of his monastery to the top of a nearby mountain. He arrives at the mountain summit exactly at sundown. The next day, he rises again at sunrise and descends down to his monastery, following the same path that he took up the mountain.
Assuming sunrise and sunset occured at the same time on each of the two days, prove that the monk must have been at some spot on the path at the same exact time on both days.
Imagine that instead of the same monk walking down the mountain on the second day, that it was actually a different monk. Let's call the monk who walked up the mountain monk A, and the monk who walked down the mountain monk B. Now pretend that instead of walking down the mountain on the second day, monk B actually walked down the mountain on the first day (the same day monk A walks up the mountain).
Monk A and monk B will walk past each other at some point on their walks. This moment when they cross paths is the time of day at which the actual monk was at the same point on both days. Because in the new scenario monk A and monk B MUST cross paths, this moment must exist.
You are standing in a pitch-dark room. A friend walks up and hands you a normal deck of 52 cards. He tells you that 13 of the 52 cards are face-up, the rest are face-down. These face-up cards are distributed randomly throughout the deck.
Your task is to split up the deck into two piles, using all the cards, such that each pile has the same number of face-up cards. The room is pitch-dark, so you can't see the deck as you do this.
How can you accomplish this seemingly impossible task?
Take the first 13 cards off the top of the deck and flip them over. This is the first pile. The second pile is just the remaining 39 cards as they started.
This works because if there are N face-up cards in within the first 13 cards, then there will be (13 - N) face up cards in the remaining 39 cards. When you flip those first 13 cards, N of which are face-up, there will now be N cards face-down, and therefore (13 - N) cards face-up, which, as stated, is the same number of face-up cards in the second pile.
You have two lengths of rope. Each rope has the property that if you light it on fire at one end, it will take exactly 60 minutes to burn to the other end. Note that the ropes will not burn at a consistent speed the entire time (for example, it's possible that the first 90% of a rope will burn in 1 minute, and the last 10% will take the additional 59 minutes to burn).
Given these two ropes and a matchbook, can you find a way to measure out exactly 45 minutes?
The key observation here is that if you light a rope from both ends at the same time, it will burn in 1/2 the time it would have burned in if you had lit it on just one end.
Using this insight, you would light both ends of one rope, and one end of the other rope, all at the same time. The rope you lit at both ends will finish burning in 30 minutes. Once this happens, light the second end of the second rope. It will burn for another 15 minutes (since it would have burned for 30 more minutes without lighting the second end), completing the 45 minutes.
You are on a gameshow and the host shows you three doors. Behind one door is a suitcase with $1 million in it, and behind the other two doors are sacks of coal. The host tells you to choose a door, and that the prize behind that door will be yours to keep.
You point to one of the three doors. The host says, "Before we open the door you pointed to, I am going to open one of the other doors." He points to one of the other doors, and it swings open, revealing a sack of coal behind it.
"Now I will give you a choice," the host tells you. "You can either stick with the door you originally chose, or you can choose to switch to the other unopened door."
Should you switch doors, stick with your original choice, or does it not matter?
You should switch doors.
There are 3 possibilities for the first door you picked:
You picked the first wrong door - so if you switch, you win
You picked the other wrong door - again, if you switch, you win
You picked the correct door - if you switch, you lose
Each of these cases are equally likely. So if you switch, there is a 2/3 chance that you will win (because there is a 2/3 chance that you are in one of the first two cases listed above), and a 1/3 chance you'll lose. So switching is a good idea.
Another way to look at this is to imagine that you're on a similar game show, except with 100 doors. 99 of those doors have coal behind them, 1 has the money. The host tells you to pick a door, and you point to one, knowing almost certainly that you did not pick the correct one (there's only a 1 in 100 chance). Then the host opens 98 other doors, leave only the door you picked and one other door closed. We know that the host was forced to leave the door with money behind it closed, so it is almost definitely the door we did not pick initially, and we would be wise to switch.
Search: Monty Hall problem
