rookie1ja
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Posts posted by rookie1ja
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Honestants and Swindlecants X. - Back to the Logic Problems
There was a girl on this island who 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.
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Honestants and Swindlecants X. - solution
„I am a poor swindlecant.“ An honestant can not say such a sentence, so it is a lie. And that’s why only a rich swindlecant can say that.
„I am not a poor honestant.“ A swindlecant can not say that, because it would be true. And that’s why an honestant who is not poor (a rich one) said that.
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Logic Problems at the Court I. - Back to the Logic Problems
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?
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Logic Problems at the Court I. - solution
Yes, the statement helped him. If he is an honestant, then a swindlecant committed the crime. If he is a swindlecant, then his statement points to an honestant who is guilty. Thus he is again innocent regarding the statement.
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Logic Problems at the Court II. - Back to the Logic Problems
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?
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Logic Problems at the Court II. - solution
The statement of plaintiff is a lie only if the hypothesis (or antecedent) is true and conclusion (or consequent) is not true. So the solicitor did not help his client at all. He actually said that his client was guilty and there was no accomplice.
Answer presented by Naruki (for explanation see below):
The correct answer is either "not enough information" or "invalid question".
Two lawyers had the following conversation.
Plaintiff: "If the prisoner is guilty, then he had an accomplice."
Solicitor: "That's not true!"
Did the solicitor help his client?h
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Logic Problems at the Court III. - Back to the Logic Problems
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?
1. 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.
2. Same situation as above, but you are the one who committed the crime.
3. 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.
4. 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?
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Logic Problems at the Court III. - solution
1. „I did it – I am guilty.“
2. There is no such sentence.
3. „I am innocent.“
4. „Either I am an honestant and innocent, or I am a swindlecant and guilty.“ = „I am either an innocent honestant, or a guilty swindlecant.“ The court could think this way:
- 4.1 If he is an honestant, then his statement is true and he is innocent.
- 4.2 If he is a swindlecant, then his statement is a lie and he is neither an innocent honestant nor a guilty swindlecant. This means that he is an innocent swindlecant.
4.3 If he is normal, then he is innocent since a normal man couldn’t have done that.
This time you are one of the inhabitants of the island. There was crime committed and people think you did it. At the court you can say only one sentence to save your life. So what do you say?
1. If you were a swindlecant (the court does not know that) and you were innocent. It is known that a swindlecant did it.
2. The same situation but you are guilty.
3. If you were an honestant (the court does not know that) and you were innocent. It is known that an honestant did it.
4. If you were innocent and everybody knows that the one who did it is not normal. Normal people sometimes lie and sometimes speak the truth. What sentence, no matter if you were an honestant, a swindlecant or normal can prove your innocence?
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Pandora's Box I. - Back to the Logic Problems
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.
Lead box
The ring is not in the golden box.
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Pandora's Box I. - solution
The given conditions indicate that only the inscription on the lead box is true. So the ring is in the silver box.
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Pandora's Box II. - Back to the Logic Problems
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.
Lead box
The ring is in this box.
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Pandora's Box II. - solution
The ring must be in the golden box, otherwise all the inscriptions would be either true or false.
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Lion and Unicorn I. - Back to the Logic Problems
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?
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Lion and Unicorn I. - solution
As there is no day when both of the beings would be lying, at least one of them must have spoken the truth. They both speak the truth only on Sunday. However, the Lion would then be lying in his statement, so it couldn’t be said on Sunday. So exactly one of them lied.
If the Unicorn was honest, then it would have to be Sunday – but previously we proved this wrong. Thus only the Lion spoke the truth when he met Alice on Thursday and spoke with the Unicorn about Wednesday.
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Lion and Unicorn II. - Back to the Logic Problems
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 said: Yesterday I was lying and two days after tomorrow I will be lying again.
Which day did he say that?
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Lion and Unicorn II. - solution
This conjunction is true only if both parts are true. The first part is true only on Thursday, but the second part is a lie then (Sunday is not a lying day of the Lion). So the whole statement can never be true (at least one part is not true). Therefore the Lion could have made the statement on Monday, on Tuesday and even on Wednesday.
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Island Baal - Back to the Logic Problems
There are people and strange monkeys on this island, and you can not tell who is who (Edit: untill you understand what they said - see below). 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.
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Island Baal - solution
Conjunction used by A is true only if both parts are true. Under the assumption that B is an honest man, then A would be honest too (B says so) and so B would be a liar as A said, which would be a conflict. So B is a liar. And knowing that, B actually said that A is a liar, too. First statement of A is thus a lie and B is not a lying monkey. However, B is lying which means he is not a monkey. B is a lying man. The second statement of A indicates that A is a monkey – so A is a lying monkey.
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Truth, Lie and Wisdom - Back to the Logic Problems
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?"
"Truth," she answered.
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.
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Truth, Lie and Wisdom - solution
Let’s assign a letter to each goddess. We get these sentences.
1. A says: B is Truth.
2. B says: I am Wisdom.
3. C says: B is Lie.
First sentence hints that A is not Truth. Second sentence is not said by Truth either, so C is Truth. Thus the third sentence is true. B is Lie and A is Wisdom.
Three goddesses were sitting in an old Indian temple. Their names were Truth (always true), Lie (always lying) and Wisdom (sometimes lying). There was the following conversation:
Asking the left one: "Who is sitting next to you?"
"Truth," she answered.
Asking the middle one: "Who are you?"
"Wisdom."
And at last question for the right one: "Who is your neighbor?"
"Lie," she replied.
Now it is clear who is who.
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In the Alps - Back to the Logic Problems
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?
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In the Alps - solution
The only one who is lying for sure is Philip. Hans speaks probably the truth and Emanuel lies. It can be also the other way, but since Hans expressed himself before Emanuel did, then Emanuel’s remark (that he does not know whether Hans is lying) is not true.
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Coins - Back to the Logic Problems
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?
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Coins - solution
"You will give me neither copper nor silver coin." If it is true, then I have to get the gold coin. If it is a lie, then the negation must be true, so "you give me either copper or silver coin", which would break the given conditions that you get no coin when lying. So the first sentence must be true.
Imagine there are 3 coins on the table. Gold, silver and copper. If you say a truthful sentence, you will get one coin. If you say a false sentence, you get nothing. Which sentence can guarantee gaining the gold coin?
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Slim Lover - Back to the Logic Problems
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?
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Slim Lover - solution
You could say for instance this sentence: „You will give me neither your photo nor a kiss.“
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Bulbs - Back to the Logic Puzzles
There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position.
How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?
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Bulbs - solution
Keep the first bulb switched on for a few minutes. It gets warm, right? So all you have to do then is ... switch it off, switch another one on, walk into the room with bulbs, touch them and tell which one was switched on as the first one (the warm one) and the others can be easily identified ...
This is one of my favorite logic puzzles (Edit: it is more a practical than a logic puzzle).
Imagine you are in a room with 3 switches. In an adjacent room there are 3 bulbs (Edit: let's say in lamps which are on a regular table) - all are off at the moment, each switch belongs to one bulb. It is impossible to see from one room to another. How can you find out which switch belongs to which bulb, if you may enter the room with the bulbs only once?
Edit: No help from anybody else is allowed.
Edit: Find out which switch belongs to which bulb - identify all 3 switches (so find out what bulbs are switches 1, 2 and 3 connected to)
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A Ping-Pong Ball in a Hole - Back to the Logic Puzzles
Your last good ping-pong ball fell down into a narrow metal pipe imbedded in concrete one foot deep.
How can you get it out undamaged, if all the tools you have are your tennis paddle, your shoe-laces, and your plastic water bottle, which does not fit into the pipe?
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Ball in a Hole - solution
All you have to do is pour some water into the pipe so that the ball swims up on the surface.
Edit:
oysterboy22's wording solution: none of those random things are going to help you, but the whole point is the person thinks they have to use the tools, while what they really have to do is urinate in the hole.
A table tennis ball (= ping pong ball) fell into a tight deep pipe (amendment: eg. 30 cm long, buried in concrete pavement - having firm metal bottom, only 1 cm of the pipe is above the ground - so it can not be moved). The pipe was only a bit wider than the ball, so you can not use your hand. How would you take it out, with no damage?
Edit:
There is another more straight forward wording (as posted by oysterboy22)
You are stuck in a room with no windows and no doors.
There is a hole in the floor about a foot deep (ok, half a meter for you non-americans) and just wider than the diameter of a table tennis ball. There is a table tennis ball at the bottom of the hole.
You have a fork, a wrench, and a long, thin plastic wire.
How do you get the ball out of the hole?
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A Man in an Elevator - Back to the Logic Puzzles
A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes to work. In the evening, when he comes back; on a rainy day, or if there are other people in the elevator, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment.
Can you explain why?
(This is one of the more popular and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions that fit the conditions, only the canonical answer is truly satisfying.)
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The Man in the Elevator - solution
The man is a of short stature. He can't reach the upper elevator buttons, but he can ask people to push them for him. He can also push them with his umbrella.
A man lives on the tenth floor of a building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator - or if it was raining that day - he goes back to his floor directly. Otherwise, he goes to the seventh floor and walks up three flights of stairs to his apartment. Can you explain why?
(This is probably the best known and most celebrated of all lateral thinking logic puzzles. It is a true classic. Although there are many possible solutions which fit the initial conditions, only the canonical answer is truly satisfying.)
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The Ball - Back to the Logic Puzzles
How can you throw a ball as hard as you can and have it come back to you, even if it doesn't bounce off anything? There is nothing attached to it, and no one else catches or throws it back to you.
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Ball - solution
Throw the ball straight up in the air.
How can you throw a ball as hard as you can and have it come back to you, even if it doesn't hit anything, there is nothing attached to it, and no one else catches or throws it?
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The Magnet - Back to the Logic Puzzles
This logic puzzle was published in Martin Gardner's column in the Scientific American.
You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?
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Magnet - solution
You can hang the iron rods on a string and watch which one turns to the north (or hang just one rod).
Gardner gives one more solution: take one rod and touch with its end the middle of the second rod. If they get closer, then you have a magnet in your hand.
The real magnet will have a magnetic field at its poles, but not at its center. So as previously mentioned, if you take the iron bar and touch its tip to the magnet's center, the iron bar will not be attracted. This is assuming that the magnet's poles are at its ends. If the poles run through the length of the magnet, then it would be much harder to use this method.
In that case, rotate one rod around its axis while holding an end of the other to its middle. If the rotating rod is the magnet, the force will fluctuate as the rod rotates. If the rotating rod is not magnetic, the force is constant (provided you can keep their positions steady).
This is a logic puzzle published in Martin Gardner's column in the Scientific American.
You are in a room where there are no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify this magnet?
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The Castle - Back to the Logic Puzzles
A square medieval castle on a square island is under siege. All around the castle there is a square moat 10 meters wide. Due to a regrettable miscalculation the raiders have brought footbridges, which are only 9.5 meters long. The invaders cannot abandon their campaign and return empty-handed.
How can the assailants resolve their predicament?
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Castle - solution
You can put one foot-bridge over one corner (thus a triangle is created). Then from the middle of this foot-bridge lay another foot-bridge to the edge (corner) of the castle. You can make a few easy equations confirming that this is enough.
A square medieval castle on a square island was under siege. All around the island, there was a 10 metre wide water moat. But the conquerors could make foot-bridges only 9.5 metres long. Nevertheless a wise man was able to figure out how to get over the water. What do you think was his advice?
(There's a place on the other side to put the bridge against, not just a sheer wall. the water moat has square corners - that section of the moat is about 14.1 metres wide.)
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Virile Microbes - Back to the Logic Puzzles
A Petri dish hosts a healthy colony of bacteria. Once a minute every bacterium divides into two. The colony was founded by a single cell at noon. At exactly 12:43 (43 minutes later) the Petri dish was half full.
At what time will the dish be full?
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Biology - solution
The dish will be full at 12:44.
Answer for old wording:
The saucer was half full at 11.59 - the next minute there will be twice as many of them there (so full at 12.00).
Let's say some primitive organisms divide themselves every minute in two equal parts that are the same size as the original organism, and which also divide the next minute and so on [wording amended]. The saucer in which we started observing this process was full at 12.00.
When was it half full?
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Sheikh's Inheritance - Back to the Logic Puzzles
An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower wins. After wandering aimlessly for days, the brothers ask a wise man for guidance. Upon receiving the advice, they jump on the camels and race to the city as fast as they can.
What did the wise man say to them?
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Sheikh’s Heritage - solution
The wise man told them to switch camels.
An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days, ask a wise man for advice. After hearing the advice they jump on the camels and race as fast as they can to the city.
What does the wise man say?
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Masters of Logic Puzzles I (dots) - Back to the Logic Puzzles
Three Masters of Logic wanted to find out who was the wisest amongst them. So they turned to their Grand Master, asking to resolve their dispute. “Easy,” the old sage said. "I will blindfold you and paint either red, or blue dot on each man’s forehead. When I take your blindfolds off, if you see at least one red dot, raise your hand. The one, who guesses the color of the dot on his forehead first, wins." And so it was said, and so it was done. The Grand Master blindfolded the three contestants and painted red dots on every one. When he took their blindfolds off, all three men raised their hands as the rules required, and sat in silence pondering. Finally, one of them said: "I have a red dot on my forehead."
How did he guess?
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Masters of Logic Puzzles I. (dots) - solution
The wisest one must have thought like this:
I see all hands up and 2 red dots, so I can have either a blue or a red dot. If I had a blue one, the other 2 guys would see all hands up and one red and one blue dot. So they would have to think that if the second one of them (the other with red dot) sees the same blue dot, then he must see a red dot on the first one with red dot. However, they were both silent (and they are wise), so I have a red dot on my forehead.
HERE IS ANOTHER WAY TO EXPLAIN IT:
All three of us (A, B, and C (me)) see everyone's hand up, which means that everyone can see at least one red dot on someone's head. If C has a blue dot on his head then both A and B see three hands up, one red dot (the only way they can raise their hands), and one blue dot (on C's, my, head). Therefore, A and B would both think this way: if the other guys' hands are up, and I see one blue dot and one red dot, then the guy with the red dot must raise his hand because he sees a red dot somewhere, and that can only mean that he sees it on my head, which would mean that I have a red dot on my head. But neither A nor B say anything, which means that they cannot be so sure, as they would be if they saw a blue dot on my head. If they do not see a blue dot on my head, then they see a red dot. So I have a red dot on my forehead.
Three masters of logic wanted to find out who was the wisest one. So they invited the grand master, who took them into a dark room and said: "I will paint each one of you a red or a blue dot on your forehead. When you walk out and you see at least one red point, raise your hands. The one who says what colour is the dot on his own forehead first, wins." Then he painted only red dots on every one. When they went out everybody had their hands up and after a while one of them said: "I have a red dot on my head."
How could he be so sure?
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Masters of Logic Puzzles II (hats) - Back to the Logic Puzzles
After losing the “Spot on the Forehead” contest, the two defeated Puzzle Masters complained that the winner had made a slight pause before raising his hand, thus derailing their deductive reasoning train of thought. And so the Grand Master vowed to set up a truly fair test to reveal the best logician amongst them. He showed the three men 5 hats – two white and three black. Then he turned off the lights in the room and put a hat on each Puzzle Master’s head. After that the old sage hid the remaining two hats, but before he could turn the lights on, one of the Masters, as chance would have it, the winner of the previous contest, announced the color of his hat. And he was right once again.
What color was his hat? What could have been his reasoning?
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Masters of Logic Puzzles II. (hats) - solution
The important thing in this riddle is that all masters had equal chances to win. If one of them had been given a black hat and the other white hats, the one with black hat would immediately have known his color (unlike the others). So 1 black and 2 white hats is not a fair distribution.
If there had been one white and two black hats distributed, then the two with black hats would have had advantage. They would have been able to see one black and one white hat and supposing they had been given white hat, then the one with black hat must at once react as in the previous situation. However, if he had remained silent, then the guys with black hats would have known that they wear black hats, whereas the one with white hat would have been forced to eternal thinking with no clear answer. So neither this is a fair situation.
That’s why the only way of giving each master an equal chance is to distribute hats of one color – so 3 black hats.
I hope this is clear enough.
The two losing masters wanted a riposte (Edit: against the winning master), so the grand master showed them 5 hats, two white and three black. Then he said: "I will turn off the light and put a hat on each of your heads and hide the other hats. When I turn on the light you will have equal chances to win. Each of you will see the hats of the two others, however not his own. The first one saying the colour of his hat will win." Then before he could turn off the light, one of the masters (the same one again) guessed, what the colour of his hat will be.
What hat was it and how did he know?
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Masters of Logic Puzzles III (stamps) - Back to the Logic Puzzles
Try this. The Grand Master takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the Grand Master's pocket and the two on his own forehead. He asks them in turn if they know the colors of their own stamps:
A: "No."
B: "No."
C: "No."
A: "No."
B: "Yes."
What color stamps does B have?
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Masters of Logic Puzzles III. (stamps) - solution
B says: "Suppose I have red-red. A would have said on her second turn: 'I see that B has red-red. If I also have red-red, then all four reds would be used, and C would have realized that she had green-green. But C didn't, so I don't have red-red. Suppose I have green-green. In that case, C would have realized that if she had red-red, I would have seen four reds and I would have answered that I had green-green on my first turn. On the other hand, if she also has green-green [we assume that A can see C; this line is only for completeness], then B would have seen four greens and she would have answered that she had two reds. So C would have realized that, if I have green-green and B has red-red, and if neither of us answered on our first turn, then she must have green-red.
"'But she didn't. So I can't have green-green either, and if I can't have green-green or red-red, then I must have green-red.'
So B continues:
"But she (A) didn't say that she had green-red, so the supposition that I have red-red must be wrong. And as my logic applies to green-green as well, then I must have green-red."
So B had green-red, and we don't know the distribution of the others certainly.
(Actually, it is possible to take the last step first, and deduce that the person who answered YES must have a solution which would work if the greens and reds were switched -- red-green.)
Try this. The grand master takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the moderator's pocket and the two on her own head. He asks them in turn if they know the colors of their own stamps:
A: "No."
B: "No."
C: "No."
A: "No."
B: "Yes."
What are the colors of her stamps, and what is the situation?
Honestants and Swindlecants IX.
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Honestants and Swindlecants IX. - Back to the Logic Problems
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?
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