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Digit Detectives

We know that every digit (0, 1, 2, …, 9) comes several times while we write the numbers from 1-100
or 1-1000, etc.

Can you figure out how many times the digit ‘3’ occurs among the numbers 1–100?
We can see digit ‘3’ in the numbers 3, 13, 23, 30, 31, 32, 33, …, 39, 43, 53, …, 93. Thus, the digit ‘3’
occurs 20 times among the numbers 1–100.

Example 3: Among the numbers 1–1000, how many times will the 230 50 810
digit ‘0’ occur? 606 704 109
Solution: Among the numbers 1–100, the digit ‘0’ will occur 11 times 400
(10, 20, 30, …., 90, 100).
Among the numbers 101–200, the digit ‘0’ will occur 20 times
(101, 102, 103, …, 109, 110, 120, 130, …., 190, 200).

Similarly, we can see in each of the numbers 201-300, 301-400, …., 801-900 the digit ‘0’ will occur
20 times and among the numbers 901-1000 it will occur 21 times.
Thus, the digit ‘0’ will occur 11 + 20 × 8 + 21 = 192 times among the numbers 1-1000.

Practice Time 3B

1. How many times will the digit ‘6’ occur among the numbers:
(a) 1–100? (b) 501–1000?
2. For the digit sum 15, write:
(a) all the 2-digit numbers

(b) any five 3-digit numbers
(c) any three 4-digit numbers

(d) any four 5-digit numbers where the digits are in ascending order
(e) the smallest 6-digit odd number
3. Calculate the digit sum of the 3-digit numbers whose

(a) any two digits are same
(b) all the three digits are same
(c) all three digits are consecutive

(d) difference between two consecutive digits are 4
4. Find the largest 5-digit number whose digit sum is 14.
5. Find the digit sum of all numbers from 31 to 79.

Formation of Numbers

Let us consider the digits 1, 3, 0 and 7.

Using these digits, let us form different 4-digit numbers in such a way that no digit is repeated in
them. Numbers may be 1307, 1370, 1037, 1073, 7310, 7130, ....

81 Number Play