This is one of my favorite logic puzzles with a real life solution.
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?
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 :-)
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?
All the tools are random things that are not going to help you. All you have to do is pour some water into the pipe so that the ball swims up on the surface. And if you say that you don't have any water, then think about what you drank today and if you can use that somehow :-)
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.)
The man is 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.
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?
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).
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?
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?
One absentminded ancient philosopher forgot to wind up his big clock hanging on the wall in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he traveled on foot to his friend's place few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock.
How did he know?
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 Puzzles (dots)
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?
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.
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?
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.
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 her own forehead. He asks them in turn if they know the colors of their own stamps:
What color stamps does B have?
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.)
Three Palefaces were taken captive by a hostile Indian tribe. According to tribe's custom they had to pass an intelligence test, or die.
The chieftain showed 5 headbands - 2 red and 3 white. The 3 men were blindfolded and positioned one after another, face to back. The chief put a headband on each of their heads, hid two remaining headbands, and removed their blindfolds. So the third man could see the headbands on the two men in front of him, the second man could see the headband on the first, and the first could not see any headbands at all.
According to the rules any one of the three men could speak first and try to guess his headband color. And if he guessed correctly - they passed the test and could go free, if not - they failed. It so happened that all 3 Palefaces were prominent logicians from a nearby academy. So after a few moments of silence, the first man in the line said: "My headband is ...".
What color was his head band? Why?
The 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.
Four angels sat on the Christmas tree amidst other ornaments. Two had blue halos and two - yellow. However, none of them could see above his head. Angel A sat on the top branch and could see the angels B and C, who sat below him. Angel B, could see angel C who sat on the lower branch. And angel D stood at the base of the tree obscured from view by a thicket of branches, so no one could see him and he could not see anyone either.
Which one of them could be the first to guess the color of his halo and speak it out loud for all other angels to hear?
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).