q 24 please answer as quick as possible
Answers
This is a nice question! I'm so much familiar with this!!!
I heard this question many times, and I answered it only as 1210.
In 1210, the first digit 1 (from left) indicates that the number contains 1 zeroes, the second digit 2 indicates that it contains 2 ones, the third digit 1 indicates that it contains 1 two, and the fourth digit 0 indicates that it contains no three!!!
There's only 1210 as the possible four digit number, and no other numbers have this property.
Why?!
Let me show you.
If the first digit is 0, it will become a three digit number. So the first digit can't be 0. So at first, let the first digit be 1.
This also means that the number contains 1 zero.
As the first digit is 1, the second digit shall be 1 because it should indicate that the no. contains 1 one.
But when the second digit becomes 1, the no. will contain 2 ones. So a contradiction occurs.
So second digit can't be 1.
When it's taken as 2, later we will get 1210. Okay.
When it's taken as 3, it indicates the no. contains 3 ones, so that the no. shall become something like 1311. But this also contradicts according to the third digit, which indicates the no. contains 1 two.
So it can't be 3.
The second digit can never be 4 or higher. If it's 4, it will indicate the no. contain 4 ones. So shan't the number be 1111???!!!
So let the first digit be 2.
Indicating that the no. contains 2 zeroes.
As the first digit number is 2, the third digit shall become 1.
So the no. will be something like 2010.
But the second digit is 0 here.
So the first digit can't be 2.
Let the first digit be 3.
So that the no. becomes something like 3000.
But the fourth digit is 0 here!!!
So, we reached our conclusion that the one and only possible four digit number is 1210.
Okay. Besides, I like to share an interesting information about this property.
There's no five digit number with this property. Neither is six digit number.
From seven digit number onwards, one number of each digit will have this property.
I mean, only one 6 digit number, one 7 digit number, one 8 digit number, one 9 digit number, etc. will have this property.
And these numbers make a pattern too! The question is asked based on this pattern!
Let me bring them.
The only one 7 digit number with this property is 3211000.
3 zeroes, 2 ones, 1 two, 1 three, 0 four, 0 five and 0 six.
The 8 digit number with this property is 42101000.
The 9 digit number with this property is 521001000.
The 10 digit number with this property is 6210001000.
Do you see any feature on these numbers?!
As saying algebraically, the first digit number of the n digit number with this property is n - 4.
E.g.: First digit of 8 digit number with this property = 8 - 4 = 4.
E.g.: First digit of 9 digit number with this property = 9 - 4 = 5.
Also, the nos. end in 3 zeroes each.
The second digit is always 2 in every nos. In 1210 too.
But such nos. are upto 13 digits, because the first digit of the 14 digit number with this property shall be 10!!! How is this possible?!
So you can write a number of any digits upto 13, by this formula, or feature.
So, I'm writing the 13 digit number with this property,
9210000001000
Hope this article helps you.
Plz mark it as the brainliest.
Plz ask me if you've any doubts.
Thank you. :-))
#adithyasajeevan