To find the next number in the sequence 9, 12, 18, 105, ?, let's analyze the pattern:

1. From 9 to 12:
   $12 = 9 + 3$

2. From 12 to 18:
   $18 = 12 \times 1.5$

3. From 18 to 105:
   $105 = 18 \times 5.83$
   This factor is unusual, so let’s check other possibilities.

It appears that the progression is inconsistent with simple arithmetic or geometric sequences, suggesting a different or more complex pattern, potentially based on multiplication and addition rules combined or skipping patterns.

Further clarification is needed regarding the potential rule or theme behind this sequence. Would you like a more detailed exploration of possible number sequence patterns?

Here are five related questions:

1. Could the numbers involve alternating rules (addition, multiplication)?
2. Are there sequences that involve prime numbers or factorials?
3. Could the jumps between the numbers indicate a mathematical series or equation?
4. Is the sequence influenced by specific divisibility rules?
5. Could a non-linear or modular approach fit the pattern better?

Tip: When faced with irregular sequences, it can help to look for alternating patterns or secondary sequences embedded within the main one.