To visit the Republic Day Parade on 26th January 2005, the people from every nook and corner including intellectuals, artists, farmers and mathematicians thronged in New Delhi. There were 100 seats in front row numbered 1, 2, 3, …, 100. But the smart mathematician chose not to sit on those seats which are the multiples of any number greater than unity. How many mathematician could sit on these front row chairs?

Options

A. a.25
B. b.26
C. c.33
D. d.none of these

Answer

To determine how many mathematicians could sit on the front row chairs, we need to identify the seats that are not multiples of any number greater than 1. This means we are looking for prime numbers and the number 1, as prime numbers are defined as numbers greater than 1 that have no divisors other than 1 and themselves.

### Step-by-Step Solution:

1. **Identify the Range of Seats**:
The seats are numbered from 1 to 100.

2. **Understand the Criteria for Seating**:
Mathematicians will not sit on seats that are multiples of any number greater than 1. This means they will only sit on prime numbers and the number 1.

3. **List the Prime Numbers from 1 to 100**:
The prime numbers in this range are:
- 2
- 3
- 5
- 7
- 11
- 13
- 17
- 19
- 23
- 29
- 31
- 37
- 41
- 43
- 47
- 53
- 59
- 61
- 67
- 71
- 73
- 79
- 83
- 89
- 97

4. **Include the Number 1**:
Since the mathematicians also include the number 1, we add it to our list.

5. **Count the Eligible Seats**:
The prime numbers from 1 to 100 are 25 in total (2 through 97), and including the number 1 gives us:
- Total = 25 (prime numbers) + 1 = 26.

6. **Conclusion**:
Therefore, the total number of mathematicians that could sit on these front row chairs is **26**.