Find two numbers whose product is a 1-digit number and the sum is a 2-digit number.

Answer

To solve the problem of finding two numbers whose product is a one-digit number and whose sum is a two-digit number, we can follow these steps:

### Step 1: Understand the requirements
We need to find two numbers, let's call them \( A \) and \( B \), such that:
- The product \( A \times B \) is a one-digit number (i.e., between 0 and 9).
- The sum \( A + B \) is a two-digit number (i.e., between 10 and 99).

### Step 2: Identify possible candidates for \( A \) and \( B \)
Since the product must be a one-digit number, we can start by considering pairs of numbers that when multiplied give a result between 0 and 9. The one-digit numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

### Step 3: Test pairs of numbers
Let's test some pairs of numbers:
1. **Pair (1, 9)**:
- Product: \( 1 \times 9 = 9 \) (one-digit)
- Sum: \( 1 + 9 = 10 \) (two-digit)

This pair satisfies both conditions.

2. **Pair (2, 4)**:
- Product: \( 2 \times 4 = 8 \) (one-digit)
- Sum: \( 2 + 4 = 6 \) (not a two-digit)

3. **Pair (3, 3)**:
- Product: \( 3 \times 3 = 9 \) (one-digit)
- Sum: \( 3 + 3 = 6 \) (not a two-digit)

4. **Pair (0, 9)**:
- Product: \( 0 \times 9 = 0 \) (one-digit)
- Sum: \( 0 + 9 = 9 \) (not a two-digit)

From these tests, we can see that the pair \( (1, 9) \) is the only one that satisfies both conditions.

### Step 4: Conclusion
Thus, the two numbers we are looking for are **1 and 9**.

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