The Legend of the Gordian Knot         Knot.bmp (34398 bytes)
At the end of a prosperous reign, the King of Phrygia died, leaving no heir. The Phrygians, distraught and without leadership, decided to send some of their people on a long, dangerous journey to the Oracle at Delphi to ask for a prophecy.

The Oracle told the people that their next king would arrive drawn by oxen. When they returned to Phrygia, the emissaries described what they had heard, and as they told the news, Gordius and his wife rode into town on their oxen-drawn wagon. In keeping with the Oracle's declaration, the elders made Gordius king.

Upon being made king, Gordius dedicated his wagon to the deity of the Oracle. To remind himself of his humble beginnings, he tied the wagon to a post in front of his palace with an enormous knot.

Gordius ruled well. And in time, his son Midas took the throne. Phrygia prospered. But when Midas stepped from the throne, he left no heir to rule in his stead. Once again, the people were without a leader. Once again, they made the difficult trip to consult the Oracle. This time the Oracle told them that he who unraveled the knot tied by Gordius would be their next ruler.

Many years passed, and many men tried to untie the famous Gordian knot. None succeeded.

Then one day in the winter of 333 B.C. Alexander the Great travelled to Phrygia flanked by a large army. First Alexander attempted to untie the knot like everyone else.

How can you help Alexander? According to the legend, the knot is the only obstacle standing in the way of him from being King of Asia.  How can you help Alexander? What are some of your suggestions?

Here are some example suggestions that have been provided by those who’ve attempted to solve this challenge:

a. choose one chord in the knot and follow it to its end, painting the chord with a bright color as you go along to keep track of it.
b. drop the knot in water until it loosens the knot up. 
c. shake the knot vigorously. 

Can you guess what Alexander did? Click on the Gordian knot pictured on top of the page and you will find out.

When it became apparent that conventional means would not work, Alexander drew his sword and sliced the knot in half. The elders of Phrygia were initially wary of his solution, but they crowned him king.

As the years passed and Alexander conquered Asia, it became evident that his unconventional solution was the first of many wise decisions.

 

 

Cowboys

A Western rancher, finding himself well advanced in years, called his boys together and told them that he wished to divide his herds between them while he still lived. 

"Now, John," he said to the eldest, "you may take as many cows as you think you could conveniently care for, and your wife Nancy may have one ninth of all the cows left."

To the second son he said, "Sam, you may take the same number of cows that John took, plus one extra cow because John had the first pick. To your good wife, Sally, I will give one ninth of what will be left."

To the third son he made a similar statement. he was to take one cow more than the second son, and his wife was to have one ninth of those left. The same applied to the other sons. Each took one cow more than his next oldest brother, and each son's wife took one ninth of the remainder.

After the youngest son had taken his cows, there were none left for his wife. Then the rancher said: "Since horses are worth twice as much as cows, we will divide up my seven horses so that each family will own livestock of equal value."

How many cows did the rancher own, and how many sons did he have ?

 

 

Cowboys

The rancher has fifty-six cows, and seven sons.

The eldest son took two cows, and his wife took six. The next son took three cows, and his wife five. the next son took four and his wife four, and so on down to the seventh son who took eight cows, leaving none for his wife. Curiously, each family now has eight cows, so each took one of the seven horses to make their livestock of equal value.

 

 

Clever Prisoner

A prisoner waits on death row. The night before his execution, he is offered a possible reprieve. Before him are two large urns. One urn contains fifty black balls, the other fifty white balls. Tomorrow, the executioner will, while blindfolded, draw a ball randomly from one of the two urns. If it's black, it's curtains for the prisoner. If it's white his sentence will be commuted to life.

The prisoner wants very much to live, and is pleased that with the current state of affairs his chances of living are fifty-fifty. He is then presented with an option. He may change the contents of the urns. He can swap white balls for black, move balls from urn to urn, etc. There is a stipulation that when he is done, there must be fifty white and fifty black balls total between the two urns. He can't eat some of the black balls or paint them or anything.

It occurs to the prisoner he might be able to help his situation by moving the balls so that there were twenty-five of each color in each urn, then making sure the white balls were on top. But the executioner might have guessed this, and may shake up the urns. Worse yet, he might deliberately reach to the bottom of the urn he chooses.

Is there another way the prisoner can help himself?

Clever Prisoner

The prisoner moves all the balls save for one white ball into one urn. There is a fifty-fifty chance that the guard will select this urn and save his life, in the other urn there is a 49:99 chance of being saved. This moves his net chance of survival up to a hair under 75%.

 

 

Light Switches

Your brand new home has a problem. On the top floor are three standing lights. On the ground floor are three switches which control the lights, presently all in the "Off" position. You don't know which switch controls which light, except that there is a one-to-one correspondence. You're down on the ground floor and want to label the switches but you want to do it in as few trips up stairs as possible. What is the minimum number of trips it takes ? 

Luckily for you, one trip is all that is needed.

Turn two switches to the "ON" position. Wait a few minutes. Turn off one of the two switches. When you reach the three lamps on the top floor, one light will be on, one light will be off and cool, one light will be off, but still warm.

 

Hats On Head

The three wisest sages in the land were brought before the king to see which of them were worthy to become the king's advisor. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits.

Led blind-folded into a small room, the sages were seated around a small wooden table as the king described the test for them.

"Upon each of your heads I have placed a hat. Now you are either wearing a blue hat or a white hat. All I will tell you is this- at least one of you is wearing a blue hat. There may be only one blue hat and two white hats, there may be two blue hats and one white hat, or there may be three blue hats. But you may be certain that there are not three white hats."

"I will shortly remove your blind folds, and the test will begin. The first to correctly announce the color of his hat shall be my advisor. Be warned however, he who guesses wrongly shall be beheaded. If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom."

With that, the king uncovered the sages' eyes and sat in the corner and waited. One sage looked around and saw that his competitors each were wearing blue hats. From the look in their eyes he could see their thoughts were the same as his, "What is the color of my hat?"

For what seemed like hours no one spoke. Finally he stood up and correctly named the hat on his head. What colour was it, and how did he know ?

 

 

Hats On Head

His hat was blue.

This is a true test for the cleverest sage since any one them could have come up with the answer. To show this is the case, consider a situation which we knew was not the case, that there was exactly one blue hat. What would happen? There would be a split second of pondering by the person wearing that hat, and he would say "I am wearing a blue hat" as he can only see two white.

Our sages worked this out for themselves, and so knew there could not be only one blue hat in the game.

This leaves everyone wondering, "Are there two or three blue hats?"

Consider the situation where there were exactly two blue hats. This seems a very real possibility at first, after all, we can see exactly two blue hats. So everyone sits and thinks- for a little while. But if there are only two hats, then two people see one blue and one white hat. These two people will very quickly, by virtue of the other's silence, rule out the possibility that there is only one blue hat (above). One of these two lucky sages would cry blue within a few short minutes, if that long.

There only scenario which forces the three sages to sit in silence is three blue hats. Our sage, through his sharp wits was the first to reach this conclusion.

 

You are driving along in your new porche boxter car on a wild, stormy night. You pass by a bus stop, and you see three people waiting for the bus:

1. An old lady who looks as if she is about to die.

2. An old friend who once saved your life.

3. The perfect man (or) woman you have been dreaming about.

Which one would you choose to offer a ride to, knowing that there could only be one passenger in your car. Think before you continue reading. This is a moral/ethical dilemma that was once actually used as part of a job application.

You could pick up the old lady, because she is going to die, and thus you should save her first; or you could take the old friend because he once saved your life, and this would be the perfect chance to pay him back.

However, you may never be able to find your perfect dream lover again.

The candidate who was hired (out of 200 applicants) had no trouble coming up with his answer. I love this, I may actually use it sometime for an interview situation.

WHAT DID HE SAY?

He simply answered: "I would give the car keys to my old friend, and let him take the lady to the hospital. I would stay behind and wait for the bus with the woman of my dreams."

Never forget to "Think Outside of the Box."