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Get a piece of paper with dimensions 9×12 with a 1×8 rectangular hole in the middle. Then, cut the paper into two pieces that can be arranged into a square. You can print out the shape below.
The solution is shown below.
Draw 2 squares in the schoolyard in order to separate all students from each other.
The solution is shown below.
If you have 10 dots on the ground, can you always cover them with 10 pennies without the coins overlapping?
Assume the dots lie in a plane and the radius of a penny is 1. Make an infinite grid of circles with radii 1, as shown on the picture, and place it randomly in the plane.
If we choose any point in the plane, the probability that it will end up inside some circle of the grid is equal to S(C)/S(H), where S(C) is the area of a coin and S(H) is the area of a regular hexagon circumscribed around it.
In a small village, there are 100 married couples living. Everyone in the village lives by the following two rules:
One day a traveler comes to the village and finds out that every man has cheated at least once on his wife. When he leaves, without being specific, he announces in front of everybody that at least one infidelity has occurred. What will happen in the next 100 days in the village?
Let us first see what will happen if there are N married couples in the village and K husbands have cheated, where K=1 or 2.
If K = 1, then on the first day the cheating husband would get killed and nobody else will die. If K = 2, then on the first day nobody will get killed. During the second day, however, both women would think like this: “If my husband didn’t cheat on me, then the other woman would have immediately realized that she was being cheated on and would have killed her husband on the first day. This did not happen and therefore my husband has cheated on me.” Then both men will get killed on the second day.
Now assume that if there are N couples on the island and K husbands have cheated, then all K cheaters will get killed on day K. Let us examine what will happen if there are N + 1 couples on the island and L husbands have cheated.
Every woman would think like this: “If I assume that my husband didn’t cheat on me, then the behavior of the remaining N couples will not be influenced by my family’s presence on the island.” Therefore, she has to wait and see when and how many men will get killed in the village. After L days pass however and nobody gets killed, every woman who has been cheated on will realize that her assumption is wrong and will kill her husband on the next day. Therefore, if there are N + 1 couples on the island, again all L cheating husbands will get killed on day L.
Applying this inductive logic consecutively for 3 couples, 4 couples, 5 couples, etc., we see that when there are 100 married couples on the island, all men will get killed on day 100.
After you die, you somehow appear in a mystical room with two doors and two keepers inside. One of the doors leads to Heaven and the other door leads to Hell. One of the keepers is always lying and the other keeper is always saying the truth. If you can ask one of the keepers whatever question you want (you don’t know which keeper is lying and which one is truthful), how can you find your way to Heaven?
You can point your finger to one of the two rooms and ask any of the keepers the question “If I ask the other keeper whether this room leads to Heaven, would he say YES?”. If the answer is NO, go through that door, if the answer is YES, go through the other one.
Can you find the objects which are hidden in the images below?
The solution is shown below.
Get from START to END in this planet maze, created by Sean Jackson.
The solution is shown below.
You have two groups of words:
To which group does “repetitive” belong?
The first group contains self-explanatory words (known as autologicals), the second group does not. Therefore “repetitive” should belong to the first group.
In Y-town all crossroads are Y-shaped, and there are no dead-end roads. Is it true that if you start from any point in the city and start walking along the roads, turning alternatingly left and right at each crossroad, eventually you will arrive at the same spot?
Yes, it is true. If you start walking forward, eventually you will end up in a loop. It is easy to see that your entire path, including the starting spot, must belong to this loop. Therefore, eventually you will end up in the starting spot again.
On top of which number is the car parked?
You are looking at the parking lot upside-down. The numbers on the picture are from 85 to 92. The car is parked on top of 87.
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