Buzzing puzzles - I

Bulbs

This is one of my favorite logic puzzles.Imagine you are in a room with 3 switches. In an adjacent room there are 3 bulbs (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?


Ball in a Hole

A table tennis ball fell into a tight deep pipe. The pipe was only a bit wider then the ball, so you can not use your hand. How would you take it out, with no damage?


The Man in the Elevator

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.)


Ball

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?


Magnet

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?


Castle
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.)
BiologyLet's say some primitive organisms divide themselves every minute in two equal parts which also divide the next minute and so on. The saucer in which we started observing this process was full at 12.00.When was it half full?


Sheikh's Heritage

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?


Philosopher's Clock

This is an old logic puzzle. One philosopher had a clock, which he had forgotten to wind up. He had no other clock, watch, radio, TV, phone or any other device telling the time. So when his clock stopped he went to a friend, stayed there the whole night and when he came home, he knew the right time.How could he know?


Masters of Logic Puzzles I. (dots)

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?


Masters of Logic Puzzles II. (hats)

The two losing masters wanted a riposte, 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?


Masters of Logic Puzzles III. (stamps)

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?


Head Bands

Three white men were taken captive by a hostile Indian tribe. The chieftain was willing to let them go so he took them to a tepee, where there was no light. He put one head band on each of their heads (he had 3 white and 2 red - so 2 head bands were not used). Then they went out in a queue so that each man saw the head-band of those standing in front of himself (the first one did not see any head band, the second one saw the first one's head band, and the third one saw the head bands of the two others). If somebody said the colour of his head-band, they all would be free. After a quiet while one of them said: "My head-band is ...".What colour was his head band? And how would you reason it?


Christmas Tree

There were 4 angels on a Christmas tree (besides other frou-frou). Two had a blue aureole and two yellow, however none of them can see behind his head. Angel A is on the highest place and he can see angels B and C, which hang below him. Below hangs angel B, who can see only angel C under him. Angel C can't see anybody, because angel D hangs under a twig (nobody can see him and he can not see anyone either).Which one of them will be the first to guess what his own aureole is?

Answers

NOTE: Try your level best to answer the fore mentioned puzzles by yourself and later scroll for answers.

Bulbs 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 ...

Ball in a Hole All you have to do is pour some water into the pipe so that the ball swims up on the surface.

The Man in the Elevator The man is a midget. 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.
BallThrow the ball straight up in the air.

Magnet 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).

Castle 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.
BiologyThe saucer was half full at 11.59 - the next minute there will be twice as many of them there (so full at 12.00).

Sheikh’s HeritageThe wise man told them to switch camels.

Philosopher’s Clock Clocks can measure time even when they do not show the right time. You just have to wind the clock up and...We have to suppose that the journey to the friend and back lasts exactly the same time and the friend has a clock (showing the correct time) - it would be too easy if mentioned in the riddle.Now there is no problem to figure out the solution, is there?

Masters of Logic I. (dots)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.

Masters of Logic II. (hats)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 ?.

Masters of Logic III. (stamps)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.)
Head BandsThe first one (he did not see any head bands) thought this way:The last one is silent, which means, he does not know, ergo at least one of head bands he sees is white. The one in the middle is silent too even though he knows what I already mentioned. If I had a red head band, the second one would have known that he had a white head band. However, nobody says anything, so my head band is not red – my head band is white.

Christmas Tree There are 2 possible solutions:1. if angels B and C had aureole of the same color, then angel A must have immediately said his own color (other then theirs),2. if angels B and C had different colors, then angel A must have been silent and that would have been a signal for angel B, who could know (looking at angel C) what his own color is (the other one then C had).