To determine how many different four-digit codes can be made using the digits 0 through 3, we can approach this problem step by step.

Key points:

1. Four digits to choose from: The available digits are 0, 1, 2, and 3.
2. Four-digit code: The code must consist of four digits.
3. Repetition allowed: The problem does not mention any restriction against repeating digits, so each of the four digits can be used in any position of the code.

Calculation:

For each of the four positions in the code, you have 4 choices (0, 1, 2, or 3).

• For the first position: 4 choices (0, 1, 2, or 3)
• For the second position: 4 choices (0, 1, 2, or 3)
• For the third position: 4 choices (0, 1, 2, or 3)
• For the fourth position: 4 choices (0, 1, 2, or 3)

Since each position in the code is independent, the total number of different codes is:

$4 \times 4 \times 4 \times 4 = 4^4 = 256$

Thus, the person can create 256 different codes.

Would you like more details or further explanation?

Related questions:

1. What if repetition of digits is not allowed? How many codes could be made?
2. How many codes could be made if we used digits from 0 to 5 instead?
3. What is the probability of guessing the correct code on the first attempt?
4. How many 3-digit codes can be made using digits 0 through 3?
5. If each code digit could only be odd (1 or 3), how many codes are possible?

Tip:

For problems involving combinations of digits or letters, always check if repetition is allowed, as this significantly impacts the total count.