7 random numbers. Random number generator

We have a sequence of numbers consisting of practically independent elements that obey a given distribution. As a rule, uniform distribution.

You can generate random numbers in Excel in different ways and methods. Let's consider only the best of them.

Random Number Function in Excel

1. The RAND function returns a random, uniformly distributed real number. It will be less than 1, greater than or equal to 0.
2. The RANDBETWEEN function returns a random integer.

Let's look at their use with examples.

Sampling random numbers using RAND

This function requires no arguments (RAND()).

To generate a random real number in the range from 1 to 5, for example, use the following formula: =RAND()*(5-1)+1.

The returned random number is distributed uniformly over the interval.

Each time the worksheet is calculated or the value in any cell in the worksheet changes, a new random number is returned. If you want to save the generated population, you can replace the formula with its value.

1. Click on the cell with a random number.
2. In the formula bar, select the formula.
3. Press F9. AND ENTER.

Let's check the uniformity of the distribution of random numbers from the first sample using a distribution histogram.

The range of vertical values ​​is frequency. Horizontal - “pockets”.

RANDBETWEEN function

The syntax for the RANDBETWEEN function is (lower bound; upper bound). The first argument must be less than the second. Otherwise the function will throw an error. The boundaries are assumed to be integers. The formula discards the fractional part.

Example of using the function:

Random numbers with precision 0.1 and 0.01:

How to make a random number generator in Excel

Let's make a random number generator that generates a value from a certain range. We use a formula like: =INDEX(A1:A10,INTEGER(RAND()*10)+1).

Let's make a random number generator in the range from 0 to 100 in steps of 10.

You need to select 2 random ones from the list of text values. Using the RAND function, we compare text values ​​in the range A1:A7 with random numbers.

Let's use the INDEX function to select two random text values ​​from the original list.

To select one random value from the list, use the following formula: =INDEX(A1:A7,RANDBETWEEN(1,COUNT(A1:A7))).

Normal distribution random number generator

The RAND and RANDBETWEEN functions produce random numbers with a uniform distribution. Any value with the same probability can fall into the lower limit of the requested range and into the upper one. This results in a huge spread from the target value.

A normal distribution implies that most of the generated numbers are close to the target number. Let's adjust the RANDBETWEEN formula and create a data array with a normal distribution.

The cost of product X is 100 rubles. The entire batch produced follows a normal distribution. A random variable also follows a normal probability distribution.

Under such conditions, the average value of the range is 100 rubles. Let's generate an array and build a graph with a normal distribution with a standard deviation of 1.5 rubles.

We use the function: =NORMINV(RAND();100;1.5).

Excel calculated which values ​​were within the probability range. Since the probability of producing a product with a cost of 100 rubles is maximum, the formula shows values ​​close to 100 more often than others.

Let's move on to plotting the graph. First you need to create a table with categories. To do this, we divide the array into periods:

Based on the data obtained, we can generate a diagram with a normal distribution. The value axis is the number of variables in the interval, the category axis is periods.

Various lotteries, sweepstakes, etc. are often held in many groups or public pages on social networks, Instagram, etc., and are used by account owners to attract new audiences to the community.

The result of such drawings often depends on the user's luck, since the recipient of the prize is determined randomly.

To make this determination, lottery organizers almost always use an online or pre-installed random number generator that is distributed free of charge.

Choice

Quite often, choosing such a generator can be difficult, since their functionality is quite different - for some it is significantly limited, for others it is quite wide.

A fairly large number of such services are being implemented, but the difficulty is that they differ in scope.

Many, for example, are tied by their functionality to a specific social network (for example, many generator applications on VKontakte work only with links from this social network).

The simplest generators simply randomly determine a number within a given range.

This is convenient because it does not associate the result with a specific post, which means it can be used for sweepstakes outside the social network and in various other situations.

They essentially have no other use.

<Рис. 1 Генератор>

Advice! When choosing the most suitable generator, it is important to consider what it will be used for.

Specifications

For the fastest process of choosing the optimal online service for generating random numbers, the table below shows the main technical characteristics and functionality of such applications.

All applications discussed in the table are described in more detail below.

<Рис. 2 Случайные числа>

RandStuff

<Рис. 3 RandStuff>

You can use this application online by following the link to its official website http://randstuff.ru/number/.

This is a simple random number generator, characterized by fast and stable operation.

It is successfully implemented both in the format of a separate independent application on the official website, and as an application on the VKontakte social network.

The peculiarity of this service is that it can select a random number both from a specified range and from a specific list of numbers that can be specified on the site.

Pros:

• Stable and fast work;
• Lack of direct connection to a social network;
• You can select one or several numbers;
• You can only choose among the specified numbers.

Minuses:

• Inability to conduct a VKontakte drawing (this requires a separate application);
• Applications for VKontakte do not run in all browsers;
• The result sometimes seems predictable because only one calculation algorithm is used.

User reviews of this application are as follows: “We determine winners in VKontakte groups through this service. Thank you,” “You are the best,” “I only use this service.”

Cast Lots

<Рис. 4 Cast Lots>

This application is a simple function generator, implemented on the official website in the form of a VKontakte application.

There is also a generator widget for inserting into your website.

The main difference from the previous application described is that this allows you to disable the repetition of the result.

That is, when carrying out several generations in a row in one session, the number will not be repeated.

• Availability of a widget for inserting into a website or blog;
• Ability to disable result repetition;
• The presence of the “even more randomness” function, after activation of which the selection algorithm changes.

Negative:

• Inability to determine several results at once;
• Inability to select from a specific list of numbers;
• To select a winner in publics, you must use a separate VKontakte widget.

User reviews are as follows: “It works stably, it’s quite convenient to use”, “Convenient functionality”, “I only use this service”.

Random number

<Рис. 5 Случайное число>

This service is located at http://randomnumber.rf/.

Simple generator with minimum functions and additional features.

Can randomly generate numbers within a specified range (maximum from 1 to 99999).

The site does not have any graphic design, and therefore the page loads easily.

The result can be copied or downloaded with the click of a button.

Negative:

• Lack of a widget for VKontakte;
• There is no possibility of holding draws;
• There is no way to embed the result into a blog or website.

Here's what users say about this service: “A good generator, but not enough functions”, “Very few features”, “Suitable for quickly generating numbers without unnecessary settings.”

Randomus

<Рис. 6 Рандомус>

You can use this random number generator at http://randomus.ru/.

Another one, quite simple, but functional random number generator.

The service has sufficient functionality for determining random numbers, but it is not suitable for conducting draws and other more complex processes.

Negative:

• Impossibility of holding draws based on reposts of posts, etc.
• There is no application for VKontakte or a widget for the site;
• It is not possible to disable repeating results.

Various lotteries, sweepstakes, etc. are often held in many groups or publics in, etc., and are used by account owners to attract new audiences to the community.

The result of such drawings often depends on the user's luck, since the recipient of the prize is determined randomly.

To make this determination, lottery organizers almost always use an online or pre-installed random number generator that is distributed free of charge.

Choice

Quite often, choosing such a generator can be difficult, since their functionality is quite different - for some it is significantly limited, for others it is quite wide.

A fairly large number of such services are being implemented, but the difficulty is that they differ in scope.

Many, for example, are tied by their functionality to a specific social network (for example, many generator applications only work with links from this one).

The simplest generators simply randomly determine a number within a given range.

This is convenient because it does not associate the result with a specific post, which means it can be used for sweepstakes outside the social network and in various other situations.

They essentially have no other use.

Advice! When choosing the most suitable generator, it is important to consider what it will be used for.

Specifications

For the fastest process of choosing the optimal online service for generating random numbers, the table below shows the main technical characteristics and functionality of such applications.

All applications discussed in the table are described in more detail below.

RandStuff

You can use this application online by following the link to its official website http://randstuff.ru/number/.

This is a simple random number generator, characterized by fast and stable operation.

It is successfully implemented both in the format of a separate stand-alone application on the official website, and as an application in .

The peculiarity of this service is that it can select a random number both from a specified range and from a specific list of numbers that can be specified on the site.

• Stable and fast work;
• Lack of direct connection to a social network;
• You can select one or several numbers;
• You can only choose among the specified numbers.

User reviews of this application are as follows: “We determine winners in VKontakte groups through this service. Thank you,” “You are the best,” “I only use this service.”

Cast Lots

This application is a simple function generator, implemented on the official website in the form of a VKontakte application.

There is also a generator widget for inserting into your website.

The main difference from the previous application described is that this allows you to disable the repetition of the result.

That is, when carrying out several generations in a row in one session, the number will not be repeated.

• Availability of a widget for inserting into a website or blog;
• Ability to disable result repetition;
• The presence of the “even more randomness” function, after activation of which the selection algorithm changes.

User reviews are as follows: “It works stably, it’s quite convenient to use”, “Convenient functionality”, “I only use this service”.

Random number

The presented online random number generator operates on the basis of a pseudo-random number generator with a uniform distribution built into JavaScript. Integers are generated. By default, 10 random numbers are output in the range 100...999, the numbers separated by spaces.

Basic settings of the random number generator:

• Amount of numbers
• Number range
• Separator type
• Turn on/off the function of removing repetitions (duplicates of numbers)

The total number is formally limited to 1000, with a maximum of 1 billion. Separator options: space, comma, semicolon.

Now you know exactly where and how to get a free sequence of random numbers in a given range on the Internet.

Application options for a random number generator

A random number generator (RNG in JS with uniform distribution) will be useful for SMM specialists and owners of groups and communities on the social networks Instagram, Facebook, VKontakte, Odnoklassniki to determine the winners of lotteries, competitions and prize draws.

A random number generator allows you to draw prizes among an arbitrary number of participants with a specified number of winners. Contests can be held without reposts and comments - you yourself set the number of participants and the interval for generating random numbers. You can get a set of random numbers online and for free on this site, and you do not need to install any application on your smartphone or program on your computer.

Also, an online random number generator can be used to simulate tossing a coin or dice. However, we have separate specialized services for these cases.

Have you ever wondered how Math.random() works? What is a random number and how is it obtained? Imagine an interview question - write your random number generator in a couple of lines of code. So, what is it, an accident and is it possible to predict it?

I am very fascinated by various IT puzzles and tasks, and the random number generator is one of these tasks. Usually in my Telegram channel I analyze all sorts of puzzles and various tasks from interviews. The random number generator problem has gained great popularity and I wanted to perpetuate it in the depths of one of the authoritative sources of information - that is, here on Habré.

This material will be useful to all those front-end and Node.js developers who are on the cutting edge of technology and want to get into a blockchain project/startup, where even front-end developers are asked questions about security and cryptography, at least at a basic level.

Pseudo-random number generator and random number generator

This source is used to accumulate entropy and then obtain from it an initial value (seed), which is necessary for random number generators (RNG) to generate random numbers.

The Pseudo-Random Number Generator uses a single seed, hence its pseudo-randomness, while the Random Number Generator always generates a random number by starting with a high-quality random variable that is drawn from various sources of entropy.

Entropy is a measure of disorder. Information entropy is a measure of the uncertainty or unpredictability of information.

PRNG has some algorithm that can be reproduced.
RNG is the process of obtaining numbers entirely from some kind of noise, the ability to calculate which tends to zero. At the same time, the RNG has certain algorithms for equalizing the distribution.

We come up with our own PRNG algorithm

Pseudorandom number generator (PRNG) is an algorithm that generates a sequence of numbers whose elements are almost independent of each other and obey a given distribution (usually uniform).

Function* rand() ( const n = 100; const mod = 2; let i = 0; while (true) ( ​​yield i % mod; if (i++ > n) i = 0; ) ) let i = 0; for (let x of rand()) ( if (i++ > 100) break; console.log(x); )
This function generates the sequence 01010101010101... and it cannot even be called pseudo-random. For a generator to be random, it must pass the next bit test. But we don’t have such a task. Nevertheless, even without any tests we can predict the next sequence, which means that such an algorithm is not suitable, but we are in the right direction.

What if we take some well-known but non-linear sequence, for example the number PI. And as the value for the module we will take not 2, but something else. You can even think about the changing value of the module. The sequence of digits in Pi is considered random. The generator can operate using Pi numbers starting from some unknown point. An example of such an algorithm, with a PI-based sequence and a variable module:

Const vector = [...Math.PI.toFixed(48).replace(".","")]; function* rand() ( for (let i=3; i<1000; i++) { if (i >99) i = 2; for (let n=0; n But in JS, the PI number can only be displayed up to 48 digits and no more. Therefore, it is still easy to predict such a sequence, and each run of such a generator will always produce the same numbers. But our generator has already started showing numbers from 0 to 9.

We got a generator of numbers from 0 to 9, but the distribution is very uneven and it will generate the same sequence every time.

We can take not the number Pi, but time in numerical representation and consider this number as a sequence of numbers, and in order to ensure that the sequence does not repeat each time, we will read it from the end. In total, our algorithm for our PRNG will look like this:

Function* rand() ( let newNumVector = () => [...(+new Date)+""].reverse(); let vector = newNumVector(); let i=2; while (true) ( ​​if ( i++ > 99) i = 2; let n=-1; while (++n< vector.length) yield (vector[n] % i); vector = newNumVector(); } } // TEST: let i = 0; for (let x of rand()) { if (i++ >100) break; console.log(x)
This already looks like a pseudo-random number generator. And the same Math.random() is a PRNG, we’ll talk about it a little later. Moreover, each time we get a different first number.

Actually, using these simple examples you can understand how more complex random number generators work. And there are even ready-made algorithms. As an example, let’s look at one of them — this is the Linear Congruent PRNG (LCPRNG).

Linear congruent PRNG

Const a = 45; const c = 21; const m = 67; var seed = 2; const rand = () => seed = (a * seed + c) % m; for(let i=0; i<30; i++) console.log(rand())
Many programming languages ​​use LCPRNG (but not exactly this algorithm(!)).

As mentioned above, such a sequence can be predicted. So why do we need PRNG? If we talk about security, then PRNG is a problem. If we talk about other tasks, then these properties can be a plus. For example, for various special effects and graphics animations, you may need to frequently call random. And this is where the distribution of meanings and performance are important! Secure algorithms cannot boast of speed.

Another property is reproducibility. Some implementations allow you to specify a seed, and this is very useful if the sequence must be repeated. Reproduction is needed in tests, for example. And there are many other things that do not require a secure RNG.

How Math.random() works

The Math.random() method returns a pseudo-random floating point number from the range = crypto.getRandomValues(new Uint8Array(1)); console.log(rvalue)
But, unlike the Math.random() PRNG, this method is very resource-intensive. The fact is that this generator uses system calls in the OS to gain access to entropy sources (mac address, CPU, temperature, etc...).