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After a car accident, the father dies and the boy arrives at the emergency room in the hospital. Upon entering the room however, the surgeon exclaims “This is my son, I can’t operate!” How is this possible?
The surgeon is the mother of the boy.
You have to cross a long bridge which supports weight up to 180 pounds. However, you weigh 175 pounds and also carry with yourself 3 golden eggs, each of which weighs 2 pounds. How can you get to the other side?
P. S. If you leave an egg unattended, someone can steal it.
Simply juggle the eggs while crossing the bridge.
You are in Monty Hall’s TV show where in the final round the host gives you the option to open one of three boxes and to receive the reward inside. Two of the boxes contain just a penny, while the third box contains $1.000.000. In order to make the game more exciting, after you pick your choice, the rules require the host to open one of the two remaining boxes, such that it contains a penny inside. After that he asks you whether you want to keep your chosen box or to switch it with the third remaining one. What should you do?
This is the so called “Monty Hall” problem. The answer is that in order to maximize your chances of winning $1.000.000, you should switch your box. The reason is that if initially you picked a box with a penny, then after switching you will get a box with $1.000.000. If initially you picked a box with $1.000.000, then after switching you will get a box with a penny. Since in the beginning the chance to get a penny is 2/3, then after switching your chance to get $1.000.000 is also 2/3. If you stay with your current box, then your chance to get $1.000.000 will be just 1/3.
If you count carefully the number of people before the tiles scramble and after that, you will see that one person disappears. Can you explain how this is possible?
Similarly, in this picture it looks like after changing the places of the tiles in the diagram, their total area decreases by one. Can you explain this?
If you look carefully, you will notice that every person in the picture of 12 people is slightly taller than the corresponding person in the picture of 13 people. Basically, we can cut little pieces from 12 different people without making noticeable changes and arrange them into a new person.
For the second question, none of the shapes before and after the scrambling is really a triangle. One of them is a bit curved in at the hypotenuse and the other one is a bit curved out. This is barely noticeable, because the red and the blue triangle have very similar proportions of their sides – 5/2 ~ 7/3.
The following game is played under very specific rules – no pinned piece checks the opposite king. How can White mate Black in 2 moves?
First, White plays f3 and threatens mate with Qxe2. Indeed, blocking with the black rook on d4 will not help, because it will become pinned, which means that the rook on d6 will become unpinned, which will make the bishop on b6 pinned, and that will unpin the knight on c7, resulting in a mate. Below are listed all variations of the game.
1. … Rd5 2. Qxe2#
2. … Bxa5 2. Kc8#
3. … Bxc7 2. Nxc7#
4. … Bxe8 2. Kxe8#
5. … Qxe7+ 2. Kxe7#
6. … Rd2 2. Bxd2#
7. … Rxd6+ 2. Qxd6#
Warning: this puzzle involves mature themes that are inappropriate for younger audiences. If you are not an adult, please skip this puzzle.
3 men must have sex with 1 woman, but they have only 2 condoms. Each of the 4 people has some unique STD which they don’t want to transfer to the rest. What can they do?
They can start by putting the two condoms on top of each other and letting the first man use them. After that, the second man can take the inner condom out and use just the outer condom. Finally, the third man can take the removed inner condom, turn it inside out, and place it back inside the outer condom. Then he, he can use the two condoms simultaneously.
On the ground there is a stick and 10 ants standing on top of it. All ants have the same constant speed and each of them can travel along the entire stick in exactly 1 minute (if it is left alone). The ants start moving simultaneously straightforward, either towards the left or the right end of the stick. When two ants collide with each other, they both turn around and continue moving in the opposite directions. How much time at most would it take until all ants fall off the stick?
Imagine the ants are just dots moving along the stick. Now it looks looks like all dots keep moving in their initially chosen directions and just occasionally pass by each other. Therefore it will take no more than a minute until they fall off the stick. If any of them starts at one end of the stick and moves towards the other end, then the time it will take for it to fall off will be exactly 1 minute.
There are 100 prisoners in solitary cells. There is a central living room with one light bulb in it, which can be either on or off initially. No prisoner can see the light bulb from his or her own cell. Every day, the warden picks a prisoner at random and that prisoner visits the living room. While there, the prisoner can toggle the light bulb if he wishes to do so. Also, at any time, every prisoner has the option of asserting that all 100 prisoners have already been in the living room. If this assertion is false, all 100 prisoners will be executed. If it is correct, all prisoners will be set free.
The prisoners are allowed to get together one night in the courtyard and come up with a plan. What plan should they agree on, so that eventually someone will make a correct assertion and will set everyone free, assuming the warden will bring each of them an infinite number of times to the central living room?
First, the prisoners should elect one of them to be a leader and the rest – followers. The first two times a follower visits the living room and sees that the light bulb is turned off, he should turn it on; after that he shouldn’t touch it anymore. Every time the leader visits the living room and sees that the light bulb is turned on, he should turn it off. After the leader turns off the lightbulb 198 times, this will mean that all followers have already visited the room. Then he can make the assertion and set everyone free.
In the Padurea forest there are 100 rest stops. There are 1000 trails, each connecting a pair of rest stops. Each trail has some particular level of difficulty with no two trails having the same difficulty. An intrepid hiker, Sendeirismo has decided to spend a vacation by taking a hike consisting of 20 trails of ever increasing difficulty.
Can he be sure that it can be done?
He is free to choose the starting rest stop and the 20 trails from a sequence where the start of one trail is the end of a previous one.
Place one hiker in each of the rest stops. Now, go through the trails in the forest one by one, in increasing difficulty, and every time you pick a trail, let the two hikers in its ends change places. This way the 100 hikers would traverse 2000 trails in total, and therefore one of them would traverse at least 20 trails.
In how many equal pieces can you cut a round cake using only 3 slices?
Eight pieces. Cut the cake into four identical pieces with two vertical slices and then make a third horizontal slice through the center.
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