A rope, burning from one end, takes 1 hour to burn out. Now you need to use this rope and a box of matches to measure for half an hour without looking at your watch. You may think it's easy. You just need to make a mark in the middle of the rope, and then measure the time it takes for the rope to burn halfway. Unfortunately, however, this rope is not uniform. Some places are thick and some places are thin, so this rope burns at different speeds in different places. It may take only 5 minutes for half of the rope to burn, and 55 minutes for the other half to burn. Faced with this situation, it seems impossible to accurately measure 30 minutes with the rope above, but this is not the case, so we can use an innovative method to solve the above problem, that is, ignite from both ends of the rope at the same time. The rope must take 30 minutes to burn out.
The problem of train running in the opposite direction
The two trains travel in opposite directions along the same track, and the speed of each train is 50 miles per hour. When the distance between two carriages is 100 mile, a fly flies from train A to train B at the speed of 60 miles per hour. When it meets the train B, it immediately turns around and flies to the train A, and so on until the two trains collide and crush the fly into pieces. How far did the fly fly before it was crushed to death?
We know that the distance between two cars is 100 miles, and the speed of each car is 50 miles per hour. This means that each car has traveled 50 miles, that is, two cars collided one hour later. During the short time from the train to the collision, the fly kept flying at 60 miles per hour, so when the two cars collided, the fly flew 60 miles. Whether the fly flies in a straight line, along a "Z" line or rolls in the air, the result is the same.
The eighth floor
Flipping a coin is not the fairest.
Flipping a coin is a common way to make a decision. People think this method is fair to both sides. Because they think that the probability of coins falling backwards is the same as that of coins falling backwards, both of which are 50%. Interestingly, this very popular idea is not correct.
First of all, although it is unlikely that a coin will stand on the ground when it falls, this possibility exists. Secondly, even if this small possibility is ruled out, the test results show that if you flick the coin with your thumb in a conventional way, the probability that the coin will still be up when it hits the ground is about 5 1%.
The reason why this happens is that with a flick of the thumb, sometimes the money will not turn over, but will only rise like a trembling flying saucer and then fall. If the next time you want to choose which side of the coin in the coin toss's hand is facing up, you should look at which side is facing up first, so that you have a greater chance of guessing correctly. But if that person is holding coins and turning his fists one by one, then you should choose the opposite from the beginning.
Probability of the same Amanome
Suppose you are attending a wedding of 50 people, someone may ask, "I wonder what is the probability that two people here are in the same Amanome?" The same here refers to the same Amanome, for example, on May 5th, but it doesn't mean that the birth time is exactly the same. "
Perhaps most people think that this probability is very small, and they may try to calculate it, guessing that this probability may be one in seven. However, the correct answer is that there are about two guests whose birthdays are on the same day attending the wedding. If the birthdays of this group of people are evenly distributed at any time in the calendar, the probability that two people have the same birthday is 97%. In other words, you have to attend 30 parties of this size to find a party without the same birthday.
One of the reasons why people are surprised is that they are puzzled by the probability that two specific people have the same birth time and any two people have the same birthday. The probability that two specific people are born at the same time is one in 365. The key to answer this question is the size of the group. As the number of people increases, the probability that two people will be in the same Amanome will be higher. Therefore, in a group of 10 people, the probability of two people in the same Amanome is about 12%. In a gathering of 50 people, the probability is about 97%. However, only when the number rises to 366 (one of whom may have been born on February 29th) can you be sure that the two people in this group must be the same Amanome.
How many socks can you make a pair?
The answer to the question how many pairs of socks can be paired is not two. And not just in my house. Why is this happening? That's because I can guarantee that if I take out two socks, black and blue, from the drawer on a dark winter morning, they may never be a pair. Although I am not very lucky, if I take out three socks from the drawer, I will definitely have a pair of socks of the same color. Whether the socks are black or blue, there will be a pair of the same color in the end. In this way, with the help of one more sock, the mathematical rules can overcome Murphy's law. From the above situation, it can be concluded that the answer to "how many socks can make a pair" is three.
Of course, this is only true if the socks are two colors. If there are blue, black and white socks in the drawer, take out a pair of socks with the same color, at least four pairs. If there are 10 pairs of socks with different colors in the drawer, you must take out 1 1 pairs of socks. According to the above situation, the mathematical rule is: If you have n kinds of socks, you must take out N+ 1 to ensure that you have an identical one in Shuang Yi.