How much can you count with your hand?

We have a very powerful mathematical tool that always carries with you - that is the hands. Like a basic computer, hands allow us to count numbers in many ways. However, counting by hand does not seem to have much effect because we have only 10 fingers.

Imagine if you want to count the hair on President Trump's hands with your hands, you will need more fingers, though the hair of the president is not. We are not saying that you NEED to do that, but sometimes it is quite convenient for you to use a couple of countless hands.

However, in fact, you don't need to have more than 10 fingers, you can still count up to a very high number. So join Science ABC to find out how high you can count with your hands!

10 fingers give us 10 objects.

Each human hand has 5 fingers, or more accurately, it consists of a thumb and four fingers. Therefore, for both hands, it is very easy for us to count to 10. In this case, there is no need to count in order and there is no need to take a finger as a mold. You can count down or count down depending on your preferences, as long as you ensure "one finger is not counted twice".

Amateur level: 24

Most people often use three knuckles to count more. Each burn is counted by a count, a 4-finger hand without a thumb as a "counting tool" will allow you to count up to 12. Therefore, by this method, with your hands you will count get 24 numbers. When using this counting method, there is no special finger priority. Just use your thumb as a counting tool, you can count the fingers in order from near to far, remotely close as you like, as long as the above rule: a knuckle is not counted twice.

Taking advantage of knuckles will help us count more.

Professional qualification: 576

In some places, one hand is used to count the other hand. More specifically, with this method, you use one hand to count points to count the knuckles of the other hand. For example, you use your left hand as a "landmark counter" , and your right hand is a "repeat counter" . To begin, count the knuckles of your right hand, and when the count reaches 12, you touch your left finger on the first knuckle on your left hand. Then you continue to count from 1 to 12, then touch the next knuckle of your left hand. Just like that, with 12 knuckles in your right hand and 12 knuckles in your left hand, you can confidently count up to 12 * 12 = 144 already.

This approach will also help us count more if we consider the lines of separation of knuckles as well as a counting unit. Each finger has three burns, corresponding to three finger splitting lines. In other words, each of our fingers can count 6 numbers, and one hand allows us to count 6 * 4 = 24 numbers. Therefore, with the above method, you can count 576 numbers.

Professional qualification: 1023

Now we will advance to some of the more complex maths in finger counting. The smartest mathematicians, when showing their talent in computing, use the "position symbol" technique . This method comes from mathematical knowledge of the decimal system: every number in the decimal system has a certain way to represent itself. In other words, all the numbers we use every day are denoted by a set of operations related to powers of 10.

Example: Number 257 is indicated by the operation: 2 * 102 + 5 * 101 + 7 * 100

The power of binary marks the importance of fingers.

Likewise, if we use binary for fingers to count, then the number 86 will be represented as 1010110, which is interpreted as changing to decimal as follows: 1 * 26 + 0 * 25 + 1 * 24 + 0 * 23 + 1 * 22 + 1 * 21 + 0 * 20.

Because our fingers have only two basic positions: folding and stretching, therefore, counting by the decimal system is very difficult, if not impossible. Therefore, we can use binary based on powers of 2 to assign values ​​to each finger one: the stretched finger is counted as 1, and the finger folds count to 0. This method helps you denotes the number of total powers of 2 (from exponent 0 to power 9 - corresponding to 10 fingers) multiplied by the number indicated by each finger (0 or 1). And if all the fingers are stretched, the highest number we can count is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023.

Computers use binary to convert and understand decimal number numbers, because they can only understand two digital signals are HIGH and LOW. HIGH is interpreted as 1, and LOW is interpreted as 0. This proves that, by all means, no matter how complex it is, can be done with binary. Of course, our 10 fingers don't have such great power, but only stop at 1023 as mentioned above.

The computer only uses and understands two HIGH and LOW signals.

In addition to the benefits of applying computing techniques based on the above symbol, we also need to show its limitations. If you want to say you need 4 bananas, then giving you 4 fingers indicates how many bananas you need will be easy to understand and give the impression of the opposite person faster. If you denote the number 22 by raising your middle finger, it doesn't seem reasonable, because the opposite person will understand another implication. And in some cases, you may be in trouble because of how you represent this number.

However, this method is quite potential when used to calculate basic operations with slightly older students. Counting on binary using fingers shows that you can count more than 10 and make a quick multiplication by the number 2 and the powers of 2.

Scientist level: positive infinity

If a person is skillful enough to be able to bend his fingers in three knots (not only to stop at two fold and stretch positions), will they raise their counting beyond 1053. By stretching Such clever fingers, the counting base is no longer 2, but 3. Therefore, the number they can count up to 59058 (= 310-1). Great.

Now we have seen that human hands are very useful in counting numbers. If our fingers create more and more shapes, we can count more numbers. The methods we put above are based on the fact that we always need visual cues about numbers represented by the shape and number of our fingers given. Of course, if we ignore the way of counting fingers but only count on touches, we can count far to infinity.

For example, if we use our thumb to lightly touch the other fingers to count, turn off the fingers, come back from the first finger and continue counting, how many will we count? OK. In theory, with this method, the higher the number, the easier it is to confuse. However, in fact, the people we count in this way are wonderful and professional!