What's special in 2020

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As the title of post contain the 2020 ,many of you might be wondering about the COVID 19 and Lockdown and thinking what's special in it dude. But let me explain that this has nothing to do with all such events ,its something special other than this . The number 2020 tells about itself , Yes , Give me a couple of minutes and i will explain all the stuff.



2020
0    1     2    3 

  • The first number 2 tells the no of times 0's is coming in the number, ie 0 is coming two times in the number
  • The second number 0 tells the no of times 1's is coming in the number, ie 1 is not in the number
  • The third number 2 tells the no of times 2's is coming in the number, ie 2 is coming two times in the number
  • The fourth number 0 tells the no of times 3's is coming in the number,ie 3 is not in the number
What's special in 2020


You are right if you think that such a number should be pompous self-centered whose only purpose in life is to describe itself. The no 2020is not only in the list 21200,3211000 are some of its types. These numbers are known as Autobiographical Numbers .
While i was going through a Youtube videos i encountered a video on this topic from Ted Ed.The basic definition of an autobiographical number N is that the first digit of N counts the no of zeroes in it ,second digit of N counts no of ones, third counts two's and so on. The smallest number of this type is 1210 and there are many more in the list. 

Now dive a bit deep into these numbers and understand them 

  • A number of given base b is b digits long ,that means 1210 is of base 4 ,and similarly for 2020 also. 21200 is of base 5.
  • There's another tricky information hidden in these no which some of you might figured it out . It is that a number of base b has sum of its digits equals to b . 2020 and 1210 both of base 4 have sum of its digits equals to 4 and 21200 in base 5 have sum of its digits equals to 5 and so on.
  • It should have atleast one zero .As self-respecting integers do not start with a zero hence, the number of zeroes is not a zero. 
  • Sum of all the digits, except for the first one, is equal to the number of non-zero digits plus 1.
  • That means, other than the first digit, the set of all other non-zero digits consists of several ones and 1 two.
  • There are no autobiographical number numbers in bases 1, 2, 3 or 6. This is based on study made by mathematicians.
  • In bases 7 and above, there is, if nothing else, a self-descriptive number of the form , which has b−4 instances of the digit 0, two instances of the digit 1, one instance of the digit 2, one instance of digit b - 4, and no instances of any other digits. The following table lists some self-descriptive numbers in a few selected bases:
Base          Autobiographical Numbers
4                             1210,2020
5                               21200
7                             3211000
8                           42101000
9                          521001000
10                     Find it yourself !
11                       72100001000
12                      821000001000

At last I am leaving you with enough information to find a autobiographical number of base 10 ,comment it down.

From now on I will also be writing on mathematical and logical puzzles and leave you with a bonus riddle

Bonus Riddle 1
What's special in 2020




Link for my youtube channel  My Youtube channel 




Thanks for reading till now
Stay Tuned :)


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