Puzzles Description

A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution. Puzzles are often contrived as a form of entertainment, but they can also stem from serious mathematical or logistical problems — in such cases, their successful resolution can be a significant contribution to mathematical research.
Solutions to puzzles may require recognizing patterns and creating a particular order. People with a high inductive reasoning aptitude may be better at solving these puzzles than others. Puzzles based on the process of inquiry and discovery to complete may be solved faster by those with good deduction skills.

History:

The first jigsaw puzzle was created around 1760, when John Spilsbury, a British engraver and mapmaker, mounted a map on a sheet of wood that he then sawed around each individual country. Spilsbury used the product to aid in teaching geography. After catching on with the wider public, this remained the primary use of jigsaw puzzles until about 1820^.
By the early 20th century, magazines and newspapers found that they could increase their daily subscriptions by publishing puzzle contests.

A puzzle undone, which forms a cube.

Puzzle cube; a type of puzzle.

An example of a British-style crossword puzzle.

 

 

 

 

 

Contemporary puzzles

A sample of notable puzzle authors includes Sam Loyd, Henry Dudeney, Boris Kordemsky and, more recently, David J. Bodycombe, Will Shortz, Lloyd King and Martin Gardner.
There are organizations and events catering to puzzle enthusiasts such as Ravenchase, the International Puzzle Party, the World Puzzle Championship and the National Puzzlers' League. There are also Puzzlehunts like Maze of Games or the Rittenhouse Chronicles.
The Rubik's Cube and other combination puzzles are toys based on puzzles that can be stimulating toys for kids and are a recreational activity for adults. Puzzles can be used to hide or obscure objects. A good example is a puzzle box used to hide jewelry.
Games are often based on a puzzle. For example there are thousands of computer puzzle games and many letter games, word games and mathematical games which require solutions to puzzles as part of the gameplay. One of the most popular puzzle games is Tetris.
A chess problem is a puzzle that uses chess pieces on a chess board.

Types of puzzles

The large number of puzzles that have been created can be divided into categories, for example a maze is a type of tour puzzle. Other categories include construction puzzles, stick puzzles, tiling puzzles, transport puzzles, disentanglement puzzles, jigsaw puzzles, lock puzzles, folding puzzles, combination puzzles and mechanical puzzles.
A meta-puzzle is a puzzle which unites or incorporates elements of other puzzles. It is often found in puzzlehunts.

• Logic puzzles using a chess board, such as Knight's Tour and Eight queens.
• Lateral thinking puzzles, which can be open ended and sometimes referred to as situation puzzles, or 'closed' lateral thinking puzzles which are designed to have only one correct and obvious answer. (See also Lloyd King).
• Mathematical problems such as the missing square puzzle. Many of these are "impossible puzzles", such as the Seven Bridges of Königsberg, Water, gas, and electricity and Three cups problem. See List of impossible puzzles.
• Picture puzzles, such as sliding puzzles like the fifteen puzzle; jigsaws and variants such as Puzz-3D.
• Word puzzles, including anagrams, crosswords and ciphers.
• Connect the dots
• Nonograms (Gridders, Paint by numbers, Hanjie, etc.)
• Peg solitaire
• Rubik's Cube
• Sangaku
• Sokoban
• Soma cube
• Spot the difference
• Tangram
• Tower of Hanoi
• Logic puzzles published by Nikoli: Sudoku, Slitherlink, Kakuro, Fillomino, Hashiwokakero, Heyawake, Hitori, Light Up, Masyu, Number Link, Nurikabe, Ripple Effect, Shikaku and Kuromasu; see List of Nikoli puzzle types
• Puzzle video game

 

 

010:Make a square from 13 units of square

Figure A is made of 8 units of square and Figure B is made of 5 units of square. Please Cut A into 3 pieces and cut B into 2 pieces and then rearrange these 5 pieces to make a square.

(The purpose of the dotted lines is to depict square units)

I will post the answer on 10th october 2010

009. Reverse the number by multiplying 7

What a magic number 7 is! It can reverse the digit sequence of a 4 digit number. A, B, C, D and E are distinct single digit numbers. What is the 4 digit number ABCD?

I will post the answer on 10th october 2010

008 Life Door or Death Door

There is a prisoner who is about to be executed. The king decides to give him one last chance to live.

There are 2 doors, the life door and the death door. There is one guard standing by each door. Those two guards know which door is the life door and which is the death door. However, one of them always tells the truth and the other always tells a lie. There is no way you can identify which door is the life door or the death door. There is no way you can distinguish who is the one telling the truth.

The prisoner can only ask one guard one question. Then he needs to choose a door to walk in. If he walks in the death door, then he will be executed. If he walks in the life door, he can have a new life.

He did choose the life door and lived. What was the question he asked? How did he choose the door after he got the answer from one of the guards?

I will post the answer on 10thoctober 2010

007. Flipping Coins

There are twenty coins sitting on the table, ten are currently heads and tens are currently tails. 

You are sitting at the table with a blindfold and gloves on. You are able to feel where the coins 

are, but are unable to see or feel if they heads or tails. You must create two sets of coins. Each 

set must have the same number of heads and tails as the other group. You can only move or flip 

the coins, you are unable to determine their current state. How do you create two even groups 

of coins with the same number of heads and tails in each group?

006.Pirates and Gold Coins

There are five rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.
The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.
The pirate world's rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.
Pirates base their decisions on three factors. First of all, each pirate wants to survive. Secondly, each pirate wants to maximize the number of gold coins he receives. Thirdly, each pirate would prefer to throw another overboard, if all other results would otherwise be equal.
 Question: What proposal should pirate A make?

I will give you the answer after 7 days
Comment your answer if you got.

005.Elevator

The Puzzle: A Man works on the 10th floor and always takes the elevator down to ground level at the end of the day.

Yet every morning he only takes the elevator to the 7th floor and walks up the stairs to the 10th floor, even when is in a hurry.

Why?

I will post the answer after 7 days

004.The Cubes

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".

I will post the solution after 7 days

003.Two Eggs Problem

•  You are given 2 eggs.
•  You have access to a 100-storey building.
•  Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100 th floor.Both eggs are identical.
•  You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
•  Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process.

Answer: Maximum 14 drops

As a programmer your first thought may be to do something along the lines of a binary search. Go to the 50th floor drop an egg and if it breaks go to the 25th floor. Oops ... if it breaks on the 25th floor you will never find the answer. Not good!

Maybe start it the 50th floor an if it breaks start back at the 2nd floor and drop until the second egg breaks. That would work and at worst you would have made 49 drops ... first at the 50th then 2-49. Okay but not optimal.

What if it doesn't break on the 50th floor? Go to the 100th floor? You would still have a worst case the same as if it had broken on the 50th floor.

So what if you start out on say the 20th floor? If the egg doesn't break then go up to the 39th floor, etc. This way you are narrowing in without increasing your worst case.

It turns out that the most optimal floor to start on is the 14th then move up to the n+(n-1) floor (14+(14-1)=27), etc. Worst case the first egg breaks on the 14th floor and you have to go back to the 2nd floor and the second egg breaks on the 13th floor. In this case you have made 13 drops. If the egg doesn't break until you have gone all the way to the 100th floor then you have only made 12 drops. The attempts would be on floors 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99 and 100. Not to mention you still have at least one egg for breakfast :).

I'll leave it up to you math wizards out there to come up with the formula for 2 eggs and a building of N floors

002 The Emperor

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 prisoners 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?

Answer:10

10 prisoners must sample the wine. Bonus points if you worked out a way to ensure than no more than 8 prisoners die.

Number all bottles using binary digits. Assign each prisoner to one of the binary flags. Prisoners must take a sip from each bottle where their binary flag is set.

Here is how you would find one poisoned bottle out of eight total bottles of wine.

Bottle:          1          2          3         4         5         6         7          8

Prisoner A               X                               X         X                    X

Prisoner B                           X                   X                    X         X

Prisoner C                                      X                    X        X         X

In the above example, if all prisoners die, bottle 8 is bad. If none die, bottle 1 is bad. If A & B dies, bottle 4 is bad.

With ten people there are 1024 unique combinations so you could test up to 1024 bottles of wine.

Each of the ten prisoners will take a small sip from about 500 bottles. Each sip should take no longer than 30 seconds and should be a very small amount. Small sips not only leave more wine for guests. Small sips also avoid death by alcohol poisoning. As long as each prisoner is administered about a millilitre from each bottle, they will only consume the equivalent of about one bottle of wine each.

Each prisoner will have at least a fifty percent chance of living. There is only one binary combination where all prisoners must sip from the wine. If there are ten prisoners then there are ten more combinations where all but one prisoner must sip from the wine. By avoiding these two types of combinations you can ensure no more than 8 prisoners die.

One viewer felt that this solution was in flagrant contempt of restaurant etiquette. The emperor paid for this wine, so there should be no need to prove to the guests that wine is the same as the label. I am not even sure if ancient wine even came with labels affixed. However, it is true that after leaving the wine open for a day, that this medieval wine will taste more like vinegar than it ever did. C'est la vie.

001. The Most Intelligent Prince

A king wants his daughter to marry the smartest of 3 extremely intelligent young princes, and so the king's wise men devised an intelligence test.

The princes are gathered into a room and seated, facing one another, and are shown 2 black hats and 3 white hats. They are blindfolded, and 1 hat is placed on each of their heads, with the remaining hats hidden in a different room.

The king tells them that the first prince to deduce the color of his hat without removing it or looking at it will marry his daughter. A wrong guess will mean death. The blindfolds are then removed.

You are one of the princes. You see 2 white hats on the other prince's heads. After some time you realize that the other prince's are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat?

Note: You know that your competitors are very intelligent and want nothing more than to marry the princess. You also know that the king is a man of his word, and he has said that the test is a fair test of intelligence and bravery.


Answer:White

The king would not select two white hats and one black hat. This would mean two princes would see one black hat and one white hat. You would be at a disadvantage if you were the only prince wearing a black hat.

If you were wearing the black hat, it would not take long for one of the other princes to deduce he was wearing a white hat.

If an intelligent prince saw a white hat and a black hat, he would eventually realize that the king would never select two black hats and one white hat. Any prince seeing two black hats would instantly know he was wearing a white hat. Therefore if a prince can see one black hat, he can work out he is wearing white.

Therefore the only fair test is for all three princes to be wearing white hats. After waiting some time just to be sure, you can safely assert you are wearing a white hat.