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# Logic Questions and Problems

## Fork in the Road - Logic Questions

You are travelling down a country lane to a distant village. You reach a fork in the road and find a pair of identical twin sisters standing there.

• One standing on the road to village and the other standing on the road to neverland (of course, you don't know or see where each road leads).
• One of the sisters always tells the truth and the other always lies (of course, you don't know who is lying).
• Both sisters know where the roads go.

If you are allowed to ask only one question to one of the sisters to find the correct road to the village, what is your question?

## Honestants and Swindlecants I

There are two kinds of people on a mysterious island. There are so-called Honestants who speak always the truth, and the others are Swindlecants who always lie.
Three fellows (A, B and C) are having a quarrel at the market. A gringo goes by and asks the A fellow: "Are you an Honestant or a Swindlecant?" The answer is incomprehensible so the gringo gives another quite logical question to B: "What did A say?" B answers: "A said that he is a Swindlecant." And to that says the fellow C: "Do not believe B, he is lying!"
Who is B and C?

## Honestants and Swindlecants II

Afterwards he meets another two aborigines. One says: "I am a Swindlecant or the other one is an Honestant."
Who are they?

## Honestants and Swindlecants III

Our gringo displeased the sovereign with his intrusive questions and was condemned to death. But there was also a chance to save himself by solving the following logic problem. The gringo was shown two doors - one leading to a scaffold and the second one to freedom (both doors were the same) and only the door guards knew what was behind the doors. The sovereign let the gringo put one question to one guard. And because the sovereign was an honest man he warned that one guard is a Swindlecant.
What logic question can save the gringo's life?

## Honestants and Swindlecants IV

Our gringo was lucky and survived. On his way to the pub he met three aborigines. One made this statement: "We are all Swindlecants." The second one concluded: "Just one of us is an honest man."
Who are they?

## Honestants and Swindlecants V

In the pub the gringo met a funny guy who said: "If my wife is an Honestant, then I am Swindlecant."
Who is this couple?

## Honestants and Swindlecants VI

When the gringo wanted to pay and leave the pub, the bartender told him how much his drink costed. It was quite expensive, so he asked the bartender if he spoke the truth. But the gringo did not hear the whispered answer so he questioned a man sitting next to him about it. And the man said: "The bartender said yes, but he is a big liar."
Who are they?

## Honestants and Swindlecants VII

Going out of the pub, the gringo heard about a fantastic buried treasure. He wanted to be sure so he asked another man who replied:
"On this island is a treasure, only if I am an honest man."
So shall he go and find the treasure?

## Honestants and Swindlecants VIII

Thinking about the treasure, the gringo forgot what day it was, so he asked four aborigines and got these answers:
A: Yesterday was Wednesday.
B: Tomorrow will be Sunday.
C: Today is Friday.
D: The day before yesterday was Thursday.
Because everything you need to know is how many people lied, I will not tell. What day of the week was it?

## Honestants and Swindlecants IX

After a hard day the gringo wanted some time to relax. But a few minutes later two aborigines wanted to talk to him. To make things clear, the gringo asked: "Is at least one of you an honestant?" After the answer, there was no doubt.
Who are they and who answered?

## Honestants and Swindlecants X

There was a girl on this island, and everybody wanted her. However, she wanted just a rich swindlecant. If you were a rich swindlecant, how would you convince her saying only one sentence? And what if she wanted a rich honestant (and if you were one). Let us assume for this logic problem that there are only rich or poor people on the island.

## Logic Problems In the Court of Law I

And now a few cases from the island of honestants and swindlecants. A prisoner at the bar was allowed to say one sentence to defend himself. After a while he said: "A swindlecant committed the crime."
Did it rescue him?

## Logic Problems In the Court of Law II

A man accused of a crime, hired an attorney whose statements were always admitted by the court as undisputable truth. The following exchange took place in court.
Prosecutor: "If the accused committed the crime, he had an accomplice."
Defender: "That is not true!"
Did the attorney help his client?

## Logic Problems In the Court of Law III

You live on an island where there are only two kinds of people: the ones who always tell the truth (truth tellers) and those who always lie (liars). You are accused of crime and brought before the court, where you are allowed to speak only one sentence in your defense. What do you say in each of the following situations?

• If you were a liar (the court does not know that) and you were innocent. And it is an established fact that a liar committed the crime.
• Same situation as above, but you are the one who committed the crime.
• If you were a truth teller (the court does not know that) and you were innocent. And it is an established fact that a truth teller committed the crime.
• If you were innocent and it is an established fact that the crime was not committed by a "normal" person. Normal people are that new immigrant group who sometimes lie and sometimes speak the truth. What sentence, no matter whether you were a truth teller, liar, or normal, can prove your innocence?

## Pandora's Box I

Once upon a time, there was a girl named Pandora, who wanted a bright groom so she made up a few logic problems for the wannabe. This is one of them.
Based upon the inscriptions on the boxes (none or just one of them is true), choose one box where the wedding ring is hidden.

Golden box
The ring is in this box.
Silver box
The ring is not in this box.
The ring is not in the golden box.

## Pandora's Box II

And here is the second test. At least one inscription is true and at least one is false. Which means the ring is in the...

Golden box
The ring is not in the silver box.
Silver box
The ring is not in this box.
The ring is in this box.

## Lion and Unicorn I

Alice came across a lion and a unicorn in a forest of forgetfulness. Those two are strange beings. The lion lies every Monday, Tuesday and Wednesday and the other days he speaks the truth. The unicorn lies on Thursdays, Fridays and Saturdays, however the other days of the week he speaks the truth.
Lion: Yesterday I was lying.
Unicorn: So was I.
Which day did they say that?

## Lion and Unicorn II

Lion said: Yesterday I was lying and two days after tomorrow I will be lying again.
Which day did he say that?

## Island Baal

There are people and strange monkeys on this island, and you can not tell who is who. They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

## Truth, Lie and Wisdom

Three goddesses were sitting in an old Indian temple. Their names were Truth (always telling the truth), Lie (always lying) and Wisdom (sometimes lying). A visitor asked the one on the left: "Who is sitting next to you?"
Then he asked the one in the middle: "Who are you?"
"Wisdom."
Lastly, he asked the one on the right: "Who is your neighbor?"
"Lie," she replied.
And then it became clear who is who.

## In the Alps

Three tourists have an argument regarding the way they should go. Hans says that Emanuel lies. Emanuel claims that Hans and Philip speak the same, only doesn't know whether truth or lie.
So who is lying for sure?

## Coins

Imagine there are 3 coins on the table: gold, silver, and copper. If you make a truthful statement, you will get one coin. If you make a false statement, you will get nothing.
What sentence can guarantee you getting the gold coin?

## Slim Lover

Something to relax. A slim young man asked a girl on a date:
"I say something. If it is truthful, will you give me your photo?"
"Yes," replied miss.
"And if it is a lie, do not give me your photograph. Would you promise that?"
The girl agreed. Then the chap said such a sentence, that after a little while of thinking she realized, that if she wanted to honor her promise, she wouldn't have to give him a photo but a kiss.
What would you say (if you were him) to be kissed and so on?