 # Hints for Assignment Q1 of Saral Module 1.1

Question
Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number, etc. until the tenth digit, which is how many 9s in the number.

Explanation of Question
The question asks us to find a 10 digit number. The digits of the number should be such that:

1st digit = Number of 0s in the number
2nd digit = Number of 1s in the number
3rd digit = Number of 2s in the number
.
.
.
10th digit = Number of 9s in the number

Example 1
Let’s take an example of a 5 digit number where the 1st digit is the number of zeros in the number.

40000

Here the number has 5 digits, and
1st digit = Number of 0s = 4

Example 2
Now let’s try to find a 10 digit number which meets all the conditions mentioned in question.

Let’s take - 9000000000

1st digit => Number of 0s = 9
2nd digit => Number of 1s = 0
3rd digit => Number of 2s = 0
.
.
.
10th digit => Number of 9s

How many 9s do we have in the above number?

1

But the 10th digit is 0 which is not equal to the number of 9s (1) in the above number.

So 9000000000 cannot be the answer.

Let’s try 8000000000
Here the first digit (8) itself is not equal to the number of 0s (9) in the number.
So we need to remove one zero and and maybe add 1 in place.

1st digit = Number of 0s = 8 is correct now
2nd digit = Number of 1s = 1 is also correct
.
.
.
9th digit = Number of 8s

How many 8s do we have in above number?

1

But the 9th digit is 0 which is not equal to the number of 8s (1) in the above number.

and if we put 1 at the 9th digit position the number will become

8100000010

But then 2nd digit = Number of 1s is 1 while there are two 1s in the number.

So this also fails.
But not many numbers are remaining to be checked.

Now it’s your chance, try with other numbers such as 7000000000, 6000000000, … 1000000000 and try to find the correct answer.

Also let us know in comments if something is not clear.

7 Likes

first we want 10 digit number it will follow all condition like in first digit how many zeros and then second digit how many 1s …etc. but if we take 9000000000 this number so first we check that first digit(9) = numbers of 0s =9 this is correct .
then second digit (0)=numbers of 1s =0 this is correct .
then 3rd digit (0)=numbers of 2s=0 this is correct.
but till we will come on 10th digit so
10th digit (0)= numbers of 9s = 1 because 9 number is came one time so it is wrong.

i’m trying again …