Islanders again...

On a certain island, the culture dictated that wives stayed home, and men did "business". The society  also dictated that if a man found out his wife was cheating, she was humiliated and kicked out by the next morning. Once a week, there was a market, and the men gossiped. It was taboo to tell a man about his wife, but other than that everyone found out about everything no later than a week after it happened.
Once, a merchant came to the island and walked around at the market. Because this was an important merchant, the islanders asked him to give a speech at the end of his stay. They were all flattered by his compliments ("What a wonderful town," etc.), but surprised to hear that he knew that there were unfaithful wives on the island.
Seven weeks later, all the unfaithful wives had been kicked out. On the seventh market day after this, there was a big announcement. "There are no more unfaithful wives on the island."
There was no polygamy on the island.
How many unfaithful wives were there originally?

Wonky Scale...

A farmer badly in need of money has decided to sell walnuts. He has a brick that weighs exactly 1 kilogram and a wonky lever balance: the distances are different. A customer comes and asks for 2 kg of walnuts.

The farmer thinks that if he puts the the weight in the left pan and measures out walnuts to balance it out, then switches the walnuts and the weight, and adds the two amounts of walnuts, he'll have the two kilograms.
Is he right?

If not, then how is it possible to measure the two kilograms?

Happy Birthday

"The day before yesterday I was 10 years old, and next year I'll turn 13."

Could this be the truth?
If yes, then how?

Lift

A person walks into an elevator on the first floor, goes up eleven floors, gets out, and walks up four flights of stairs. This person does this every day. Why?

The lift goes up to the top of the building (say 20 floors), and the person isn't crazy, or badly in need of exercise. 

The answer will be at answersdiscarded.blogspot.com someday.

How to slice a cake

This is one of the easier math problems that requires either one good look or several minutes' worth of squinting at it and trying to force your mind to think out of the box.  To many mathematicians, the answer seems obvious as soon as they hear the problem, but for some people, it takes awhile.

How to cut a generic birthday cake into eight pieces in no more than three straight cuts? No special tools or anything.

The answer is at answersdiscarded.blogspot.com.

Please, please, please try to think of the answer before looking it up.

Wise People

On a distant planet, far across the galaxies, a mighty ruler decided to test her wise people to find out which one of them was the wisest. She invited them to her planet,  and offered them wine and food.  The wise people, whose talents were much unappreciated,  had not seen so much food in all of their lives, and were soon sound asleep.  When the wise people woke up, they all saw that everyone's faces were colored green, but they could not see their own faces. They all immediately started laughing, and so did the ruler, quietly laughing behind her secret spot under a table loaded with dessert.
But then one stopped, and then another.
They all gradually stopped laughing, realizing that they, too must have paint on their faces.
The ruler named the first one to stop her prime minister.

Question: how did the wise people find out that they, too had been colored green?
Hint: try deciding on a number of wise people.

The answer is at answersdiscarded.blogspot.com.

PLEASE THINK ABOUT IT BEFORE YOU LOOK IT UP.

Knights and Knaves (starting easy)

     I think that this may be my favourite type of math/logic riddle.  In a world where there are only knights and knaves...

Knights can only tell the truth.  Knaves can only lie.

     You are on an island with two towns, walking  along a road. One town is where all the knaves live, and the other is where all the knights live. You have to post a letter to your friend, but there is only one post office, and it's in the knights' town.
     You have come to a fork: one road leads to the knaves' town and the other to the knights' town. You see a man sitting at the fork, but you do not know whether he is a knight or a knave.  On this peculiar island, you are always allowed to ask one question to another person.  You have to ask him a question which determines which town is the knights' town.  Remember: you do not know whether he is a knight or a knave.


This is one of the easier questions of this type. Again, the answer is at discardedlogic.blogspot.com, answer number 5.  PLEASE TRY TO FIND THE ANSWER before looking it up. (!)

Princess' Groom

      In a faraway kingdom, the beautiful princess, daughter of the mighty (and unjust) ruler, subject of the courting of many princes and even kings from even farther away kingdoms, suddenly fell in love.  This was a completely new feeling for her, and she really didn't know what to do.  After many hours of thinking and rethinking, forced to use parts of her lovely little head which were normally left idle, the poor creature decided to tell her maid, an elderly woman with much experience. She immediately told the girl to confess to the fortunate man. Little did the maid know that the subject of the princess' love was a swineherd.
      The swineherd, a very sharp young man who hoped to do great things and had already taught larger part of the royal pig population the times two table, reacted very strangely indeed.  Instead of dressing up in furs and gold, bringing gifts to the king, and sucking up to the princess (as did all of her previous suitors), he responded by kissing her. On the whole, thought the princess, happily (and muddily) returning home, it was a most productive evening.
      After about half a year's worth of such evenings, the king found out.  He immediately ordered the poor swineherd's execution and the princess' marriage to the baldest king on the planet. No pleading or tears from his daughter could change his mind. However, his chief counselor advised him that maybe it would be a good idea to appear merciful to his people. He suggested that the condemned man should be publicly given a choice of two papers which he would blindly draw from a bag, and which would determine whether he should be executed or allowed to marry the princess. To make sure that he would die, both papers would have "guilty" written on them.
      The princess, hearing only the first part of the plan, immediately ran to find her beloved in the dungeons.  He, being an optimistic young man, rejoiced and said that it was better than no chance at all.  However, the princess soon found out about the trickery. In tears, she told her swineherd all about it.  Instead of being discouraged, he told her that the fates had turned their way, and he was to be soon united with her for the rest of their lives.
      How?
      Write your answers in comments, but try not to read other people's comments before thinking yourselves.
      I have put the answer on answersdiscarded.blogspot.com. Answer #3.

Please, please, please think about it before looking at the answer.  (!)

Zmei Gorynych

Ivan-Tsarevitch: A charming young prince, whose strength and bravery are known to every simpleton in the tsardom.
Zmei Gorynych: A three-headed dragon-serpent who/which dies in a couple fairy-tales and math problems. He/It likes pretty ladies and exactly what he/it does to them is unknown.
Old Lady: The wisest and most trusted people in Russian fairy-tales. Counsel-givers and rumor-spreaders.

Ivan-Tsarevitch, tired of having his "friends" carried off by the dreaded Zmei Gorynych decided to save his town by challenging him to a duel.  Now, Zmei Gorynych had no great desire to see Ivan-Tsarevitch's legendary strength firsthand, so he proposed a duel of wits, "to add a little variety", and Ivan-Tsarevitch was very relieved that he didn't have to spoil anyone's slightly modified view of his strength.
   An old lady had once told Ivan-Tsarevitch that around Zmei Gorynych's dwelling there are many streams, nine of which are poisoned. Each of these was numbered and if you drink some water from  one of the streams, then water from a stream with a greater number works as antidote. There is a tenth stream, inside Zmei Gorynych's cave, which beats all.
   Zmei Gorynych said that they should meet near the old oak tree, bringing with them water from a stream.  Each would give this water to the other duelist. This duelist was then to go and do whatever he/it could to prolong his/its survival. Zmei Gorynych was very proud of his plan, as he knew what he would do: bring water from the tenth stream that only he could access and give Ivan-Tsarevitch some. When Ivan-Tsarevitch gave him some water, he would drink some of the tenth stream, counter-acting whatever Ivan gave him.  A fool-proof plan, right?
   The next day, Ivan-Tsarevitch and Zmei Gorynych met, drank each other's water, and then went off. In half an hour, Ivan-Tsarevitch was good as new, and Zmei Gorynych was dead, poisoned.

 How? Where did Zmei Gorynych's plan go wrong?

For the answer, which I really hope you don't look up because you're gonna feel stupid if you do, go to answersdiscarded.blogspot.com, and I'm not putting it as a link, so that you'll think about it. Answer number two. 

The Riddle of the Three Doors

     You are a noble prince, and you are on a quest to save your beloved princess. The wicked Dragon has captured her and locked her up in his dark tower.  None have yet defeated this vile creature, but nothing will stop your determination to challenge it.  However, the monster had two cups of strong, rich, coffee this morning, and is feeling benign.  It leads you up to three doors, and says:
  "Two of these doors have tigers behind them, but one leads to your princess. You can choose."
One out of three is a poor chance for such a valiant prince, but fighting the dragon you stand no chance at all,  so you sigh and step towards a door.
  "Stop.  Two cups of coffee have made me soft indeed," says the Dragon, "About the door you are about to open I will say nothing, but behind THIS door," he opens a door just a crack so that you can see the tiger within, "contains a tiger."

Now cometh the tricky part. Should you, prince, step away from the door you chose and open the other one (not the one that the Dragon opened, but the one that's left), or should you proceed and just open the one you were about to open?

THAT is the question.

Not some to be or not to be...


To find the answer, go to answersdiscarded . blogspot . com, and no, I'm not putting it as a link, so that you have SOME time to think about the riddle. (answer number 1).