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In London, many Underground tube stations have two escalators going up, but just one going down. Why?
This is because when people leave the train, they pack into groups, whereas when they go to catch the train, their flow is evener.
King Octopus has servants with 6, 7, or 8 legs. The servants with 7 legs always lie, and the servants with 6 or 8 legs always tell the truth. One day four of the king’s servants had the following conversation:
“We together have 28 legs,” said the first octopus.
“We together have 27 legs,” said the second octopus.
“We together have 26 legs,” said the third octopus.
“We together have 25
Which of the four servants told the truth?
If all four octopuses lied, then their total number of legs must be 28, which is impossible. Therefore exactly one of them said the truth, and the other three had 7 legs each. Since the truthful octopus must have 6 or 8 legs, and 21 + 8 = 29, we see that it has exactly 6 legs, and therefore it is the second one.
You are in a room with nothing else but two indistinguishable iron rods. You know that one of them is magnetized, how can you figure out which one?
Touch the middle of the first rod with the end of the second rod. If the two rods get attracted to each other, then the second one is the magnet. If not, then the first one is the magnet.
If the day before yesterday Tim was 18 years old and next year he will be 21 years old, what is the date today?
Today is 1st of January.
Get from START to FINISH in this landscape maze, created by Matthew Haussler.
The solution is shown below.
John: “I know every song in the World.”
Paul: “It can’t be. I bet you don’t know any songs which contain the name of my daughter – Beatrice.”
John accepted the bet and won. Which song did he sing?
John performed the “Happy Birthday” song.
Oh no, zombies are attacking your house!
Every second, a new zombie drops down on one of the 9 spots of your lawn, which is currently unoccupied. All zombies move towards your house on the left with constant speed, and each of them needs exactly 1 second to traverse a spot of the lawn. Once a zombie steps out of the lawn, it enters your house and waits there for the others (thus each zombie travels total distance between 1 and 9 spots).
Show that after some time, the total distance traversed by any 1000 consecutive zombies will be within the range of just 50 spots.
Remark: Assume your house can accommodate an unlimited amount of zombies.
Since the number of zombies on the lawn never decreases, it must stabilize at some point. Therefore after some time T, there will be exactly K zombies on the lawn at all times, 1 ≤ K ≤ 9.
Consider any 1000 consecutive zombies appearing past time T and take a picture of the lawn at the moment each of them gets dropped on it – this makes a total of 1000 pictures. Since on every picture, there are exactly K zombies, we see exactly 1000K zombies on these pictures.
Now notice that almost all of the selected 1000 zombies appear on as many pictures as lawn spots they traverse. The zombies for which this is not true are just the K zombies, which appear on the last picture. We easily see that they have traveled between 1 + 2 + … + K − 1 and (10 − K) + (11 − K) + … + 8 spots more than the number of pictures they appear on.
Similarly, on the 1000 pictures we have taken, there are K−1 additional zombies, which appear multiple times (you can see all of them on the first picture). The total number of times they show up is again between 1 + 2 + … + K − 1 and (10 − K) + (11 − K) + … + 8.
Therefore we conclude that the total distance the selected 1000 zombies travel is equal to 1000K ± {[(10 − K) + (11 − K) + … + 8] − [1 + 2 + … + K − 1]} = 1000K ± (9 − K)(K − 1).Since (9 − K)(K − 1) is a number between 0 and 16, this solves the problem.
Two friends are playing the following game – taking turns, they place identical coins on a square table, so that no two coins touch each other. Whoever can not make a move, loses the game. Who has a winning strategy?
The first player has a winning strategy. He just has to place the first coin in the center of the table and then each consecutive one symmetrically opposite to the last coin of his opponent.
In order to catch the thief, you must make your way through this Tetris maze formed by the 5 different pieces shown at the bottom. You can not climb over the blocks, just find a tunnel inside the construction.
The solution is shown below.
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