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PUZZLES
1Here is a famous prize problem that Sam Loyd issued in 1882, offering $1000 as a prize for the best answer showing how to arrange the seven figures and the eight 'dots' .4.5.6.7.8.9.0. Which would add up to 82?
2 You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned. The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison. You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned. You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed. What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?
3 A stark raving mad king tells his 100 wisest men he is about to line them up and that he will place either a red or blue hat on each of their heads. Once lined up, they must not communicate amongst themselves. Nor may they attempt to look behind them or remove their own hat. The king tells the wise men that they will be able to see all the hats in front of them. They will not be able to see the color of their own hat or the hats behind them, although they will be able to hear the answers from all those behind them. The king will then start with the wise man in the back and ask "what color is your hat?" The wise man will only be allowed to answer "red" or "blue," nothing more. If the answer is incorrect then the wise man will be silently killed. If the answer is correct then the wise man may live but must remain absolutely silent. The king will then move on to the next wise man and repeat the question. The king makes it clear that if anyone breaks the rules then all the wise men will die, then allows the wise men to consult before lining them up. The king listens in while the wise men consult each other to make sure they don't devise a plan to cheat. To communicate anything more than their guess of red or blue by coughing or shuffling would be breaking the rules. What is the maximum number of men they can be guaranteed to save?
4 You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more than the other side. What is the smallest number of times you must use the scale in order to always find the fake coin? Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale. etc. These are modern coins, so the fake coin is not necessarily lighter. Presume the worst case scenario, and don't hope that you will pick the right coin on the first attempt.
5 A 120 wire cable has been laid firmly underground between two telephone exchanges located 10km apart. Unfortunately after the cable was laid it was discovered to be the wrong type, the problem is the individual wires are not labelled. There is no visual way of knowing which wire is which and thus connections at either end is not immediately possible.
PUZZLES
You are a trainee technician and your boss has asked you to identify and label the wires at both ends without ripping it all up. You have no transport and only a battery and light bulb to test continuity. You do have tape and pen for labeling the wires. What is the shortest distance in kilometers you will need to walk to correctly identify and label each wire?
6 I ask Alex to pick any 5 cards out of a deck with no Jokers. He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Peter can't see any of this). I look at the cards and I pick 1 card out and give it back to Alex. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Peter. Peter looks at the 4 cards i gave him, and says out loud which card Alex is holding (suit and number). How? The solution uses pure logic, not sleight of hand. All Peter needs to know is the order of the cards and what is on their face, nothing more.
7 The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another. "In the prison is a switch room, which contains two light switches labelled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything. "After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell. "No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead. "Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.' "If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you" What is the strategy they come up with so that they can be free?
8 Acting on an anonymous phone call, the police raid a house to arrest a suspected murderer. They don't know what he looks like but they know his name is John and that he is inside the house. The police bust in on a carpenter, a lorry driver, a mechanic and a fireman all playing poker. Without hesitation or communication of any kind, they immediately arrest the fireman. How do they know they've got their man?
9 A man lives in the penthouse of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. Upon his return, however, he can only travel halfway up in the lift and has to walk the rest of the way - unless it's raining. What is the explanation for this?
10 A man walks into a bar and asks for a drink of water. The bartender thinks for a minute, pulls out a gun and points it at him. The man says, "Thank you," and walks out.
PUZZLES
11 Each morning I appear To lie at your feet, All day I will follow No matter how fast you run, Yet I nearly perish In the midday sun.
12 You have a three gallon and a five gallon measuring device. You wish to measure out four gallons.
13 A corporate businessman has two cubes on his office desk. Every day he arranges both cubes so that the front faces show the current day of the month. What numbers are on the faces of the cubes to allow this? Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07".
14 Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start travelling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
15 Four Tasmanian camels travelling on a very narrow ledge encounter four Tasmanian camels coming the other way. As everyone knows, Tasmanian camels never go backwards, especially when on a precarious ledge. The camels will climb over each other, but only if there is a camel sized space on the other side. The camels didn't see each other until there was only exactly one camel's width between the two groups. How can all camels pass, allowing both groups to go on their way, without any camel reversing?
16
A guy picked a book off the highest shelf in a library. On the spine, he read "How to Jog". He ran out of the room and opened the book but found it had absolutely nothing to do with jogging. Explain...
17
Eternally I am 1 to 6, eternally am 15 to 20, I am always 5, but I am never ever 21 unless I am flying, what am I???
18
A man lives on the 18th floor of his complex. He takes the elevator all the way to the top on days that are rainy. He goes to the 12th floor and walks up if he's alone on the elevator. Why is that?
19
I walk into a room where there are 10 people in who are 20 years old 10 who are 19, 10 who are 18 and 10 who are 30. How many people are there in the room?
20 There are three boxes. One is labelled "APPLES" another is labelled "ORANGES". The last one is labelled "APPLES AND ORANGES". You know that each is labelled incorrectly. You may ask me to pick one fruit from one box which you choose. How can you label the boxes correctly?
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