Using the digits 1,2,3,4,5 to create a 4 digit number sequence by combining two of the digits in the middle of the sequence, beginning with the second digits in the sequence, example;   1, 23,4, 5 or 2, 34, 5, 1 or 4, 51, 2, 3...list all possible combinations in order

To solve this problem, we need to create all possible combinations of a 4-digit sequence using the digits 1, 2, 3, 4, and 5. The rules are:

1. We will select four digits.
2. One of these four digits will actually be a two-digit number formed by combining two adjacent digits from the set.
3. The two-digit number must be placed starting with the second position in the sequence.
4. The remaining digits are placed around this two-digit number to form the final sequence.

We'll list all the possible combinations in order, making sure that each sequence is unique.

### Steps:
1. We start by selecting which pair of digits will form the two-digit number.
2. After selecting the two-digit number, we arrange the remaining three digits around it.

Let's list all the combinations.

### Combinations:

1. **1, 23, 4, 5**
2. **1, 24, 3, 5**
3. **1, 25, 3, 4**
4. **2, 13, 4, 5**
5. **2, 14, 3, 5**
6. **2, 15, 3, 4**
7. **2, 34, 1, 5**
8. **2, 35, 1, 4**
9. **3, 12, 4, 5**
10. **3, 14, 2, 5**
11. **3, 15, 2, 4**
12. **3, 24, 1, 5**
13. **3, 25, 1, 4**
14. **4, 12, 3, 5**
15. **4, 13, 2, 5**
16. **4, 15, 2, 3**
17. **4, 23, 1, 5**
18. **4, 25, 1, 3**
19. **5, 12, 3, 4**
20. **5, 13, 2, 4**
21. **5, 14, 2, 3**
22. **5, 23, 1, 4**
23. **5, 24, 1, 3**
24. **5, 34, 1, 2**
25. **5, 35, 1, 2**
  
This is a complete list of all the possible combinations where two of the digits are combined into a two-digit number placed in the second position.

Do you have any further questions or need additional details?

### Related Questions:
1. What happens if the two-digit number can be placed in any position, not just the second?
2. How would the number of combinations change if we had 6 digits instead of 5?
3. How many sequences are possible if we do not combine any digits at all?
4. What if we could combine any two adjacent digits, not necessarily starting from the second position?
5. How many combinations are possible if the order of the digits does not matter?

### Tip:
When listing combinations, creating a systematic pattern like always starting with the smallest digit helps ensure that you do not miss any possibilities.

Using the digits 1,2,3,4,5 to create a 4 digit number sequence by combining two of the digits in the middle of the sequence, beginning with the second digits in the sequence, example; 1, 23, 4, 5 or 2, 34, 5, 1 or 4, 51, 2, 3...list all possible combinations in order

Learn how to create all possible 4-digit number sequences using the digits 1, 2, 3, 4, and 5 by combining two adjacent digits in the middle of the sequence. This combinatorics problem helps understand permutations and how to systematically list combinations. Suitable for students in Grades 6-8.

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