The problem involves the numbers 1, 2, 3, 4, and 5, each being used at least once, and placed in the given boxes to satisfy the two equations:

1. [ ] + [ ] = [ ]
2. [ ] × [ ] = [ ]

We are asked to determine which number is used twice to satisfy these equations.

Steps to Solve:

1. Analyze the operations:

   • In the addition equation, the result should fall within the range of 3 to 9 because:
     • Minimum sum: $1 + 2 = 3$,
     • Maximum sum: $4 + 5 = 9$.
   • In the multiplication equation, the result should fall within the range of 2 to 20 because:
     • Minimum product: $1 \times 2 = 2$,
     • Maximum product: $4 \times 5 = 20$.

2. Check all possibilities:

   • Each number can only be used once except one number, which is used twice.
   • A solution must satisfy both equations.

Test possible solutions:

Let us try possible combinations by testing which number could be repeated. After testing:

The only valid solution is:

• 4 + 5 = 9, and
• 2 × 4 = 8.

In this solution, the number 4 is used twice.

Final Answer:

The number that is used twice is D) 4.

Would you like me to explain the testing process in more detail or assist with a similar question?

Here are 5 related questions to explore further:

1. How can we systematically solve equations involving repeated digits?
2. What are some other examples of equations requiring unique digits?
3. Can these types of problems be solved using programming or algorithms?
4. How would the solution change if more than one number could repeat?
5. What is the mathematical principle behind constraints like these?

Tip: When solving problems with unique and repeated digits, start by testing boundary cases to narrow down possibilities.