Here's the scenario: You're an explorer who's just stumbled upon a trove of valuable coins in a remote dungeon. Each coin has a gold side and a silver side, each with an identical scorpion seal. The wizard who guards the coins agrees to let you have them, but he won't let you leave the room unless you separate the hoard into two piles with an equal number of coins with the silver side facing up in each. You've just counted the total number of silver-side-up coins—20—when the lights go out. In the dark, you have no way of knowing which half of a coin is silver and which half is gold. How do you divide the pile without looking at it?
The task is fairly easy to complete, no psychic powers required. All you need to do is remove any 20 coins from the pile at random and flip them over. No matter what combination of coins you choose, you will suddenly have a number of silver-side-up coins that's equal to whatever is left in the pile. If every coin you pulled was originally gold-side-up, flipping them would give you 20 more silver-side-up coins. If you chose 13 gold-side-up coins and seven of the silver-side coins, you'd be left with 13 silver coins in the first pile and 13 silver ones in your new stack after flipping it over.
The solution is simple, but the algebra behind it may take a little more effort to comprehend. For the full explanation and a bonus riddle, check out the video from TED-Ed below.
Cannibals ambush a safari in the jungle and capture one hundred men. The cannibals give each captive a single chance to escape uneaten.
Each captive is wearing a hat which is either white or black. The captives are lined up in order of height, and are tied to stakes, all facing forward towards the captive in front of him. Each captive can see the hats of all captives in front of him, but cannot see his own hat or hats of prisoners standing behind him.
The chief cannibal is going to ask the color of each captive’s hat starting from the last captive in the rear of the line. If a captive tells the correct color then he is released, otherwise, he is executed.
How many captives can be saved at most if they are allowed to discuss a strategy before the jailer starts asking colors of their hats?
The Solution:
At-most 99 captives can be saved and the 100th captive has 50-50 chances of being saved.
The idea is that every prisoner counts number of white hats in front of him (could be either color as long as all captives have agreed ahead of time which color they’re counting).
The 100th captive says white if the number of white hats is even. He may or may not be saved, but he conveys enough information to save the 99th prisoner.
The 99th captive knows that the captive behind him counted an even number of white hats, including whatever hat the 99th captive is wearing. Therefore, if the 99th captive sees an odd number of white hats in front of him, then he knows that he must be wearing a white hat for the man behind him to have seen an even number – and he answers white. Likewise, if the 99th captive sees an even number of white hats in front of him, then he knows that his hat must be black based on the answer from the man behind him. The 99th captive yells out his answer and is spared.
The next prisoner now knows whether the remaining number of white hats, including his own, is odd or even, by taking into account whether #99 had a white hat or not. Then by counting the number of white hats he sees, he knows the color of his hat. So he yells out the color of his hat and is spared. Each remaining captive follows this logic and is spared.
Cannibals ambush a safari in the jungle and capture three men. The cannibals give the men a single chance to escape uneaten.
The captives are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back of the man in front, and the man in front cannot see anyone. The cannibals show the men five hats. Three of the hats are black and two of the hats are white.
Blindfolds are then placed over each man's eyes and a hat is placed on each man's head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed.
The man in the rear who can see both of his friends' hats but not his own says, "I don't know". The middle man who can see the hat of the man in front, but not his own says, "I don't know". The front man who cannot see ANYBODY'S hat says "I know!"
How did he know the color of his hat and what color was it?
Our Solution:
Remembering that there were only two white hats, the man in the rear could not have seen two white hats, otherwise he would have known that he was wearing a black hat. Likewise, if the man in the middle saw a white hat in front of him, then he would have known that he wore a black hat (based on the man in the back’s answer). But if the man in the middle saw a black hat in front of him, then he wouldn’t know if he himself was wearing a black or white hat. Therefore, the man in front, hearing the other two answers, knew that he must be wearing a black hat!
James Bond needs to access a secret file locked in a locker that can be accessed only by a code. The code is about 7 characters and consists of numbers and letters. There was a label on the locker as "You force heaven to be empty".
What was the code?
Answer: U472BMT
The code can be decoded to sound as "U four seven two B M T"
Snow and Tyrion are two mad logicians and loves betting.
They placed 11 Candies at the table and designed a small betting game, in which both of them need to eat Candies turn by turn with the following rules:
Rule1: One need to eat at least one candy.
Rule2: One cannot eat more than 5 candies.
The one that eats last candy will loose.
Snow won the toss and need to start.
How many candies must Snow ear in order to make sure that he won the bet?
Halloween is fast approaching! To celebrate the holiday, five neighbors traveled across town to attend different costume parties either with friends or with family. Each neighbor wore a different costume to the party and each party was held on a different street. Determine the full name of each neighbor, what costume each wore, if the party each attended was held by a friend or a relative, and the street name of where each party was held.
Clues:
Ms. Whittaker didn't wear the pirate costume. The two people who went to a relative's party were the pirate and the person whose last name was Wells
Aaron didn't go to his relative's party dressed as a Viking. The person whose last name was Wright went to the party on Redstone Road.
Martha didn't go to the party on Rice Road. Sara's last name wasn't Wentworth.
A relative held the party on Rutland Road. Sara dressed as an elf. Wayne didn't have a skeleton costume.
Aaron White didn't go to the party on River Road. The neighbor who went to a friend's party on Rabbit Road was dressed in a mummy costume.
Mr. Wells went to the party on Rice Road. Ross, whose last name wasn't Wentworth, went to a friend's party.
Four children on Byron Road dressed up for Halloween and then went out trick or treating. They each wore a different costume and collected a different number of treats.
Who dressed up in which costume and how many treats did they each collect?
Clues:
The most treats were not collected by the ghost or wizard.
Willa collected either 12 or 15 treats.
Andy, dressed as a ghost, collected more treats than at least one other person.
Lori collected more treats than at least two others, and she was not dressed as a wizard.
Mark collected more treats than Willa who wore a pumpkin outfit, but less than Lori.
The ghost collected one less treat than the wizard.
One child collected 13 treats.
The werewolf collected the most treats, which was three more than the pumpkin collected
Imagine this. It's the eve of the annual Bankers State Association Banquet. The treasurer has procured the food and the wine for the following evening's gala, and he's extremely pleased with himself because he knows a guy, who knows a guy, who knows a guy, and for only $50 he's obtained fourteen one-half gallon jugs of the finest red wine. He's very excited about the following evening's festivities until he receives an anonymous note suggesting that one of those bottles of wine may be poisoned!
Because they're hopeless cheapskates and unwilling to discard 14 bottles of perfectly good cheap wine, the bankers consult with a scientist friend of theirs. “So let's see,” he says, “you have these sixteen bottles of wine and one of them may be poisoned.”
The scientist goes on to suggest that from his knowledge of poisons, even the smallest sample is usually enough to cause certain death, even if mixed and diluted with the wine from the untainted bottles. “Hmmmmm,”' he says. “I'll be right back.”
In a flash, he returns with four small cages, each one containing your standard lab rat. “Here you go,” he says.
“But wait, wait,” they say. “We have 14 bottles of wine. How are we supposed to save all the bankers coming to the luncheon tomorrow, with just 4 rats?'”
“You can do it,” he says and then disappears into the inky shadows.
So, you have 4 rats in little cages, 14 bottles of wine and one of them may have poison in it. Now you can obviously take samples from any of the bottles and you can give as much or as little as you want to any of the rats.
The answer: You use unique combinations. With four different variables (i.e. rats) you can create 16 distinct combinations.
Here's how you do it. Bottle number one goes only to rat one. Bottle number two goes only to rat number two. Bottle number three goes only to rat number three. And bottle number four goes only to rat number four.
Here's the interesting part. Bottle number five goes to rats one and two. So if rats one AND two are belly up the next day, it can only be because bottle number five had the poison in it. Bottle number six goes to rates one and three. So if rats one AND three are belly up the next day, it can only be because bottle number six had the poison in it.
Rat
Drinks from Bottle #...
1
1, 5, 6, 7, 11, 12, 13
2
2, 5, 8, 9, 11, 12, 14
3
3, 6, 8, 10, 11, 13, 14
4
4, 7, 9, 10, 12, 13, 14
Each unique combination corresponds to a different bottle of wine. Here are tables showing what wine to give to each rat, and then how to determine which bottle is poisoned depending on which rats go to rat heaven:
Imagine you're at home in a city somewhere in the United States. You decide to travel along each of the four compass directions, north, south, east, and west. Day 1, you travel due north and you eventually cross a state line. Let's call this state X. You return home.
The next day you decide to travel due south. Again you come to the border of your home state and its neighbor. It is also state X. You return home amazed.
Day 3, you elect to proceed due east and you are shocked to find out that the first state you reach is, again, state X! On the fourth day you travel due west and soon are stupefied to find a sign saying, 'Welcome to State X'!
There is only one city in the United States whereby traveling along the four compass points, north, south, east and west, the first state you reach is identical no matter which direction you choose. Name the city and the state.
Answer: The state is New York State. And the city is Stamford, Connecticut.
No matter where you go you hit New York State. If you leave Stamford, Connecticut, and you go north, you actually hit New York State because there's a little bit of New York State that sticks out into Connecticut. And if you go west from Stamford, you clearly hit New York State. If you go south you'll hit Long Island. And if you go east you'll hit the far east end of Long Island - all of which is New York State!
A woman and her husband frequently go walking together. On one particular day, however, they walked side by side, one never getting ahead of the other. They walked for an hour. At the end of the hour, the woman says, "That felt good. I think I walked four miles. The husband responds, "Oh, I walked much farther than that. I'm sure I walked five or six."
How could that be?
Answer: The husband and wife were walking side by side each and on treadmills. And all the conditions are met. They walk side by side, one never getting ahead of the other. The husband, in order to travel a greater distance than she, just took more steps.
