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

We need to create a 4-digit number sequence using the digits 1, 2, 3, 4, and 5, with the requirement that the second and third positions in the sequence are a two-digit number formed by combining two of the digits. 

Each number sequence will look like this:

\[
a, (bc), d, e
\]

Where:
- \(a\) is the first digit
- \(bc\) is a two-digit number formed by combining two digits
- \(d\) is the third digit
- \(e\) is the fourth digit

We will go through all possible combinations by systematically arranging the digits for each position, ensuring no repetition of digits within a sequence.

Here are all the possible combinations in order:

1. \(1, 23, 4, 5\)
2. \(1, 23, 5, 4\)
3. \(1, 24, 3, 5\)
4. \(1, 24, 5, 3\)
5. \(1, 25, 3, 4\)
6. \(1, 25, 4, 3\)
7. \(1, 34, 2, 5\)
8. \(1, 34, 5, 2\)
9. \(1, 35, 2, 4\)
10. \(1, 35, 4, 2\)
11. \(1, 45, 2, 3\)
12. \(1, 45, 3, 2\)

13. \(2, 13, 4, 5\)
14. \(2, 13, 5, 4\)
15. \(2, 14, 3, 5\)
16. \(2, 14, 5, 3\)
17. \(2, 15, 3, 4\)
18. \(2, 15, 4, 3\)
19. \(2, 34, 1, 5\)
20. \(2, 34, 5, 1\)
21. \(2, 35, 1, 4\)
22. \(2, 35, 4, 1\)
23. \(2, 45, 1, 3\)
24. \(2, 45, 3, 1\)

25. \(3, 12, 4, 5\)
26. \(3, 12, 5, 4\)
27. \(3, 14, 2, 5\)
28. \(3, 14, 5, 2\)
29. \(3, 15, 2, 4\)
30. \(3, 15, 4, 2\)
31. \(3, 24, 1, 5\)
32. \(3, 24, 5, 1\)
33. \(3, 25, 1, 4\)
34. \(3, 25, 4, 1\)
35. \(3, 45, 1, 2\)
36. \(3, 45, 2, 1\)

37. \(4, 12, 3, 5\)
38. \(4, 12, 5, 3\)
39. \(4, 13, 2, 5\)
40. \(4, 13, 5, 2\)
41. \(4, 15, 2, 3\)
42. \(4, 15, 3, 2\)
43. \(4, 23, 1, 5\)
44. \(4, 23, 5, 1\)
45. \(4, 25, 1, 3\)
46. \(4, 25, 3, 1\)
47. \(4, 35, 1, 2\)
48. \(4, 35, 2, 1\)

49. \(5, 12, 3, 4\)
50. \(5, 12, 4, 3\)
51. \(5, 13, 2, 4\)
52. \(5, 13, 4, 2\)
53. \(5, 14, 2, 3\)
54. \(5, 14, 3, 2\)
55. \(5, 23, 1, 4\)
56. \(5, 23, 4, 1\)
57. \(5, 24, 1, 3\)
58. \(5, 24, 3, 1\)
59. \(5, 34, 1, 2\)
60. \(5, 34, 2, 1\)

In total, there are 60 possible combinations.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How many different combinations can you form if you combine three digits instead of two?
2. What happens if you change the number of digits used in the sequence?
3. How can you calculate the number of permutations for these kinds of combinations mathematically?
4. Can you find a way to automate this sequence generation using programming?
5. What if you impose additional constraints, such as requiring that the two-digit number be even?

**Tip**: When listing combinations, it's helpful to use a systematic method to ensure no possibilities are missed.

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.

Explore all possible 4-digit number sequences using the digits 1, 2, 3, 4, 5, where the second and third positions are a combined two-digit number. Includes a detailed breakdown of 60 combinations using permutation and combination principles. Ideal for Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation