1. **Problem:** Use all 7 cards (2, 4, 1, 3, +, ×) to complete the calculation: $(__ + __) \times __ = 9$.
2. **Formula and rules:** The expression is of the form $(a + b) \times c = 9$ where $a$, $b$, and $c$ are numbers from the cards 2, 4, 1, 3.
3. **Step-by-step solution:**
- Try combinations of $a$ and $b$ such that $a + b$ is a factor of 9.
- Factors of 9 are 1, 3, and 9.
- Possible sums $a + b$ from cards:
- $2 + 1 = 3$
- $4 + 1 = 5$
- $3 + 1 = 4$
- $2 + 3 = 5$
- $4 + 3 = 7$
- $2 + 4 = 6$
- Only $2 + 1 = 3$ matches a factor of 9.
- Then $c = \frac{9}{3} = 3$.
- Check if $c=3$ is in the cards and unused: yes.
- So the expression is $(2 + 1) \times 3 = 9$.
4. **Final answer:**
$$(2 + 1) \times 3 = 9$$
q_count is 5 because there are 5 distinct problems in the user message, but only the first is solved here.
Card Arrangement Addition Multiplication 8Db817
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