You have to descend a 100-meter vertical cliff. However, you have only a 75-meter long rope and a knife with yourself. On the top of the cliff and halfway down – 50 meters above the ground, there are two big pins stuck in it. How can you get safely down to the ground?
SOLUTION
First, you cut the rope at 25 meters and make a loop at the end of the short part. Then you pass the longer part through the loop so that you get a 50-meter long rope (the second 25 meters are doubled). You use this rope to descend to the pin and grab it. Then tie one of the ends of the 50-meter rope to the pin, pull the rest back through the loop and let it fall to the ground.
In order to see that 8 is the minimum number of moves, notice that Black could only move rooks and knights, and therefore he has made an even number of moves. This implies that White has made an odd number of moves, excluding the pawn on f3. This is possible only if he has placed his king on a white cell at some point and then returned it back to e1, which would take at least 8 moves.
Two gunshots were fired through the window of a coffee shop. When the police arrived, they successfully recognized which gunshot was fired first. Which was the first gunshot and how did they figure that out?
SOLUTION
The cracks of the left gunshot end up right at the cracks of the right gunshot. Therefore the first gunshot is the one on the right.
Take six coins and arrange them in a triangle as shown in the image. Your goal is to rearrange the coins into a hexagon with only four moves. Every move consists of sliding one coin to a new location where it touches at least two other coins.
Two very short friends, John and Jack, were living together in an apartment. Since they used to lose their apartment key very often, they decided to leave it on top of the door frame when they leave home. In order to reach the key, John was climbing on Jack’s shoulders and thus taking it down from the frame. However, John was the taller and the heavier guy of the two. Why didn’t Jack climb on top of his shoulders instead?
SOLUTION
The reason is that as being taller, John also had longer arms. If Jack climbed on John’s shoulders, he wouldn’t have reached the key.
You place two stones on a chessboard and start moving them one by one, every time shifting a stone to an adjacent cell – left, right, up, or down, without letting the stones at any time occupy the same cell. Is it possible to find such a sequence of moves, that all possible combinations for the position of the stones occur exactly once?
SOLUTION
No, such sequence does not exist. Call a position of the stones “matching” if the stones occupy cells of the same color, and “opposite” if the stones occupy cells of opposite colors. If such sequence exists, then the number of matching and opposite positions must differ by at most 1. However, the number of matching positions is 64×31, whereas the number of opposite positions is 64×32, so this is not true.
You and eight of your team members are trying to escape the Temple of Doom. You are running through a tunnel away from a deadly smoke and end up in a large hall. There are four paths ahead, and exactly one of them leads to the exit. It takes 20 minutes to explore any of the four paths one way, and your group has only 60 minutes until the deadly smoke suffocates you. The problem is that two of your friends are known to be delirious and it is possible that they do not tell the truth, but nobody knows which ones they are. How should you split the group and explore the tunnels, so that you have enough time to figure out which is the correct path and escape the temple?
SOLUTION
You explore the first path. You send two of your teammates to explore the second path. You send the remaining six teammates in groups of three to explore each of the two remaining paths. If your path leads to the exit, then everything is good. Otherwise, you ask the two groups of three whether their paths lead to the exit. If in both groups everyone answers consistently, then nobody is lying, and you will escape. If in both groups there is a person whose answer is different from the others in the group, then the majority in both groups says the truth. Once again, you will know which path leads to the exit. Finally, if in exactly one of the groups everyone answers consistently, you ask the group of two. If the team members there answer consistently with each other, then they say the truth. You will have two groups which tell the truth and will know which path leads to the exit. If the answers of the teammates in the group of two differ, then in the inconsistent group of three the majority will be saying the truth. Again, you will be able to deduce which path leads to the exit.
When a car is making a turn, are its front wheels parallel to each other?
SOLUTION
The front wheels are not parallel to each other. The reason is that when steering, all wheels are turning along arks that have a common center. Otherwise, the car would be drifting.
