Sina Technology News, Beijing time July 28. According to foreign media reports, mathematics often makes even smart people feel incredibly foolish, and sometimes it even makes them quite angry.
In fact, mathematics itself is very interesting; it is a part of our daily lives, and everyone can enjoy it. It is just that in the classroom, mathematics is often taught in a rigid way by rigid teachers. The following are some examples of fun mathematics in daily life recently published by the British newspaper The Daily Mail:
The Calculator on Your Body
When using your hands for calculation, one of the simplest forms of multiplication is for multiples of 9. There is a trick for this that children often know very well, but older people might not be as familiar with. To calculate multiples of 9, place your hands on your knees and number your fingers from left to right, as shown in the diagram. Now, choose the multiple of 9 you want to calculate; suppose the expression is 7 \times 9. Simply bend the finger labeled with the number 7, as shown in the image above. Then, count the number of fingers remaining to the left of the bent finger, which is 6, and the number of fingers remaining to its right, which is 3. Put them together, and you get the answer for 7 \times 9, which is 63.
The Probability of Sharing a Birthday
Suppose you are attending a wedding with 50 guests. Someone might ask: “I want to know what the probability is that two people here share the same birthday?” Here, “the same” refers to the same day of the year, such as May 5th, not necessarily the exact same birth year or time.
Most people might think this probability is very small. They might try to calculate it and guess that the probability is perhaps one in seven. However, the correct answer is that there will likely be about two guests at this wedding who share a birthday. If birthdays are distributed uniformly throughout the calendar, the probability that two people share the same birthday in a group of 50 is 97%. In other words, you would have to attend 30 gatherings of this size to find just one where no two guests share a birthday.
One reason people find this surprising is that they confuse the probability of two specific people having the same birthday with the probability of any two people in a group sharing a birthday. The probability of two specific people sharing a birthday is 1/365. The key to this problem is the size of the group. As the number of people increases, the probability of two people sharing a birthday rises rapidly. In a group of 10 people, the probability is about 12%. In a party of 50, it is about 97%. However, it is only when the number of people reaches 366 (accounting for someone potentially born on February 29th) that you can be 100% certain that at least two people in the group share a birthday.
How Many Socks to Make a Pair?
Regarding the question of how many socks it takes to make a pair, the answer is not two. And this isn’t just something that happens in my house. Why is that? It’s because I can guarantee that on a dark winter morning, if I pull two socks out of a drawer containing black and blue socks, they might not match. Although I might not be very lucky, if I take 3 socks out of the drawer, I can say for certain that there will be a pair of the same color. Whether that pair is black or blue, there will eventually be a matching pair. Thus, with the help of just one extra sock, the rules of mathematics can defeat Murphy’s Law. From this, we can conclude that the answer to “how many socks to make a pair” is 3.
Of course, this only holds true when there are two colors of socks. If there are three colors in the drawer—for example, blue, black, and white—you must take out at least 4 socks to ensure a matching pair. If there are 10 different colors of socks, you must take out 11. The mathematical rule summarized from this is: if you have N types of socks, you must take out N+1 socks to ensure you have a perfectly matching pair.
Timing with Burning Ropes
You have a rope that takes exactly 1 hour to burn from one end to the other. Now, without looking at a watch, you need to measure exactly half an hour using only this rope and a box of matches. You might think this is easy: just mark the middle of the rope and measure the time it takes for half the rope to burn. Unfortunately, the rope is not uniform; some parts are thicker and some are thinner, so the burning rate varies at different points. Perhaps one half of the rope takes only 5 minutes to burn, while the other half takes 55 minutes. In this situation, it seems impossible to accurately measure 30 minutes using the rope, but that is not the case. One can use an innovative method: light the rope from both ends simultaneously. The time it takes for the rope to burn out completely will be exactly 30 minutes.
The Problem of Trains Moving Toward Each Other
Two trains are traveling toward each other on the same track, each at a speed of 50 miles per hour. When the two trains are 100 miles apart, a fly starts flying from Train A toward Train B at a speed of 60 miles per hour. After it meets Train B, it immediately turns around and flies back toward Train A, and continues this back-and-forth until the two trains collide and crush the fly. How far did the fly travel in total before being crushed?
We know the two trains are 100 miles apart and each travels at 50 miles per hour. This means each train travels 50 miles, and they will collide after exactly one hour. During the hour from the trains’ departure to the collision, the fly has been flying at a constant speed of 60 miles per hour. Therefore, at the moment the trains collide, the fly has traveled 60 miles. Whether the fly flies in a straight line, a “Z” shape, or loops in the air, the result is the same.
Coin Tossing is Not Perfectly Fair
Tossing a coin is a common method for making decisions. People believe this method is fair to both parties because they assume the probability of the coin landing heads or tails is the same, 50% each. However, interestingly, this popular belief is not entirely correct.
First, while the probability of a coin landing on its edge is extremely small, the possibility exists. Second, even if we exclude that tiny possibility, test results show that if you toss a coin in the conventional way—flicking it with your thumb—the side that was facing up at the start has about a 51% chance of facing up when it lands.
This happens because when flicked with the thumb, sometimes the coin does not actually flip; it simply rises and falls like a wobbling saucer. If you are choosing which side a coin will land on next time, you should look at which side is currently facing up; your probability of guessing correctly will be slightly higher. However, if the person catches the coin and flips it onto the back of their hand, you should choose the side opposite to the one that started facing up. (By Xiao Wen)
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