Here are the solutions and explanations for the puzzles in the image:

1. Replace the question mark in the triangle

• First triangle: $7 \times 3 = 21$, then subtract 9 ($21 - 9 = 12$).
• Second triangle: Apply the same logic. $6 \times 3 = 18$, then subtract 11 ($18 - 11 = 7$).

Answer: (b) 7

2. Number series puzzle

The numbers progress as follows:

• $18 + 2 = 20$
• $20 + 4 = 24$
• $24 + 8 = 32$
• $32 + 16 = 48$

Answer: (c) 48

3. Hexagon puzzle

The numbers are prime numbers progressing in sequence:

• 5, 7, 11, 13, 17, ?
• The next prime number after 17 is 19.

Answer: (c) 19

Let me know if you need further clarification or have additional questions!

Related Questions:

1. Can you solve more puzzles involving number sequences?
2. How can prime numbers be identified quickly?
3. What are common patterns found in triangular puzzles?
4. Can you give more examples of series with incremental changes?
5. Are there more examples of combining multiplication and subtraction in puzzles?

Tip:

When solving puzzles with patterns, always check for arithmetic operations, geometric progressions, or prime sequences!