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...example .. 1, 23, 4, 5 or 1, 2, 34, 5 or 5, 4, 13, 2...list all possible combinations


To create all possible 4-digit number sequences by combining two of the digits in the middle, using the digits 1, 2, 3, 4, and 5 exactly once, here is the list of all possible combinations. You can combine the digits in two forms: either (1st, 2nd & 3rd combined, 4th) or (1st, 2nd, 3rd & 4th combined, last).

### Combinations:

#### Case 1: 1st, middle digits combined, last
1. 1, 23, 4, 5 → 1, 234, 5
2. 1, 2, 34, 5 → 1, 2, 345
3. 1, 2, 3, 45 → 1, 23, 45

4. 2, 13, 4, 5 → 2, 134, 5
5. 2, 1, 34, 5 → 2, 1, 345
6. 2, 1, 3, 45 → 2, 13, 45

7. 3, 12, 4, 5 → 3, 124, 5
8. 3, 1, 24, 5 → 3, 1, 245
9. 3, 1, 2, 45 → 3, 12, 45

10. 4, 12, 3, 5 → 4, 123, 5
11. 4, 1, 23, 5 → 4, 1, 235
12. 4, 1, 2, 35 → 4, 12, 35

13. 5, 12, 3, 4 → 5, 123, 4
14. 5, 1, 23, 4 → 5, 1, 234
15. 5, 1, 2, 34 → 5, 12, 34

### In summary:
- There are 15 possible combinations.

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Would you like more details or further explanation on this?

**Related Questions:**
1. How do you generalize this process for other sets of digits?
2. What if the positions of combined digits are unrestricted?
3. How does the problem change with more digits?
4. What is the total number of sequences if you can combine digits freely?
5. How does this change if the number of digits increases or decreases?

**Tip**: When handling combinations, systematically explore options by fixing digits in positions, then varying the remaining ones.

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... example .. 1, 23, 4, 5 or 1, 2, 34, 5 or 5, 4, 13, 2... list all possible combinations

Explore all possible ways to create a 4-digit number sequence using the digits 1, 2, 3, 4, and 5, where two digits are combined in the middle. This combinatorics problem demonstrates the use of number sequences and permutations, ideal for students in Grades 9-12.

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