Let the original cost of each puzzle be \( x \). Since the puzzles are discounted by 50¢ (or $0.50), the cost of each puzzle after the discount is \( x - 0.50 \).
Molly is buying puzzles for 6 grandchildren, so the total cost for all the puzzles is:
\[ 6(x - 0.50) = 27 \]
Now, we can solve for \( x \):
- Distribute the 6:
\[ 6x - 3 = 27 \]
- Add 3 to both sides:
\[ 6x = 30 \]
- Divide by 6:
\[ x = 5 \]
Thus, the original cost of each puzzle is:
\[ \boxed{5} \]