To solve this problem, we need to determine how many four-digit numbers can be created using the digits 1, 2, 3, and 4, where each digit can be used multiple times.

Since each digit can be used repeatedly, the calculation is straightforward.

For each of the four places in the number (thousands, hundreds, tens, and units):

• You have 4 choices (1, 2, 3, or 4) for each digit.

Therefore, the total number of four-digit numbers can be calculated as: $4 \times 4 \times 4 \times 4 = 4^4 = 256$

Thus, there are 256 different four-digit numbers that can be formed using the digits 1, 2, 3, and 4, where each digit can be repeated.

Would you like more details or have any further questions?

Here are 5 related questions to consider:

1. What if the digits must be unique in the four-digit number?
2. How many three-digit numbers can be formed using the same digits, allowing repetitions?
3. What is the number of five-digit numbers that can be formed if the digits can still be repeated?
4. How many four-digit numbers can be formed if only the digits 1, 2, and 3 are used?
5. Can you calculate the total if the four-digit number must start with an odd digit?

Tip: When repetition is allowed, you can simply multiply the number of choices for each digit's place.