Introduction

To create 4-digit numbers using the digits 2 and 3, we need to follow a few rules. We will use both digits an equal number of times, and the numbers should be 4 digits long. Let's explore how we can achieve this.

Step 1: Identify the possible combinations

To begin, let's identify all the possible combinations of the digits 2 and 3. Since we need to use both digits an equal number of times, we can have two scenarios:

1. Using each digit twice: In this case, we can have the combinations 22 and 33. These combinations will result in 4-digit numbers, as required.

2. Using each digit once: In this case, we can have the combinations 23 and 32. These combinations will also result in 4-digit numbers.

Step 2: Construct the 4-digit numbers

Now that we have identified the possible combinations, let's construct the 4-digit numbers using each combination.

1. Using each digit twice:
- 22: To create a 4-digit number using 22, we can repeat the digits. For example, we can have 2222 or 2223, depending on the desired sequence of digits.
- 33: Similarly, with 33, we can create numbers like 3333 or 3332.

2. Using each digit once:
- 23: To create a 4-digit number using 23, we can combine both digits in different orders. For example, we can have 2323 or 2332.
- 32: Likewise, with 32, we can create numbers like 3232 or 3223.

Conclusion

By following the given rules, we have successfully created 4-digit numbers using the digits 2 and 3. Remember, we used both digits an equal number of times and ensured that the numbers were 4 digits long. The combinations we obtained were 22, 33, 23, and 32, which can be further extended by repeating or rearranging the digits.

2233