The same operation(s) are followed in all the given number pairs except one. Identify the odd number pair. Note: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.

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Let's analyze each pair to find a common operation:

1. Pair (19 : 3):
   - Check if the second number is related to the first by a certain operation.
   - 19 - 16 = 3 (16 is 4 squared)
   - 19 - 16 = 3

2. Pair (55 : 9):
   - 55 - 46 = 9 (46 is not a perfect square)
   - Try dividing: 55 / 6 = 9.16 (not exact)
   - Try square root: sqrt(55) ≈ 7.4 (not 9)
   - Try sum of digits: 5 + 5 = 10 (not 9)
   - Try difference of digits: 5 - 5 = 0 (not 9)
   - Try subtracting 46 (not a perfect square), no clear pattern.

3. Pair (49 : 8):
   - 49 - 41 = 8 (41 is not a perfect square)
   - sqrt(49) = 7, 7 + 1 = 8
   - So second number = sqrt(first number) + 1

4. Pair (24 : 4):
   - sqrt(24) ≈ 4.89, close to 5, not 4
   - 24 / 6 = 4
   - 6 squared = 36, no relation

Now, check pairs 1, 3, and 4 for a common pattern:
- Pair 1: 19 - 16 = 3, where 16 = 4^2
- Pair 3: 49 - 41 = 8, 41 not a square, but sqrt(49) + 1 = 8
- Pair 4: 24 / 6 = 4

Try another approach:
- Pair 1: 19 - 16 = 3 (16 = 4^2)
- Pair 3: 49 - 41 = 8 (41 not square)
- Pair 4: 24 / 6 = 4

Try to see if the second number is the number of letters in the English word of the first number:
- 19: 'Nineteen' has 8 letters
- 3: 'Three' has 5 letters
- 55: 'Fifty-five' has 9 letters (counting hyphen as a letter or not?)
- 9: 'Nine' has 4 letters
- 49: 'Forty-nine' has 9 letters
- 8: 'Eight' has 5 letters
- 24: 'Twenty-four' has 10 letters
- 4: 'Four' has 4 letters

No consistent pattern.

Try prime factorization:
- 19 is prime, 3 is prime
- 55 = 5 * 11, 9 = 3^2
- 49 = 7^2, 8 = 2^3
- 24 = 2^3 * 3, 4 = 2^2

Try difference between first number and square of second number:
- Pair 1: 19 - 3^2 = 19 - 9 = 10
- Pair 2: 55 - 9^2 = 55 - 81 = -26
- Pair 3: 49 - 8^2 = 49 - 64 = -15
- Pair 4: 24 - 4^2 = 24 - 16 = 8

No consistent pattern.

Try difference between first number and cube of second number:
- Pair 1: 19 - 3^3 = 19 - 27 = -8
- Pair 2: 55 - 9^3 = 55 - 729 = -674
- Pair 3: 49 - 8^3 = 49 - 512 = -463
- Pair 4: 24 - 4^3 = 24 - 64 = -40

No consistent pattern.

Try dividing first number by second number:
- 19 / 3 ≈ 6.33
- 55 / 9 ≈ 6.11
- 49 / 8 ≈ 6.125
- 24 / 4 = 6

All approximately 6, except 24/4 = 6 exactly.

So the operation is: First number divided by second number ≈ 6
Except for pair 1 (19/3 ≈ 6.33), pair 2 (55/9 ≈ 6.11), pair 3 (49/8 ≈ 6.125), pair 4 (24/4 = 6 exactly)

Pair 1 is the odd one out because 19/3 is not close to 6 as others are.

Hence, the odd pair is 19 : 3.

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