Math Problem Statement
Using the digits 1,2,3,4,5 to create a 4 digit number sequence by combining two of the digits beginning with the second and using the third digit combined in the sequence...examples... 1, 23, 4, 5 and 2, 34, 5, 1 or 4, 51, 2, 3...list all possible combinations in order
Solution
To form the four-digit number sequences from the digits 1, 2, 3, 4, 5, we will follow these rules:
- You must combine two digits starting with the second digit (e.g., 23, 34, etc.).
- Then, the third digit will combine in sequence.
So, here's the full set of combinations:
- 1, 23, 4, 5
- 1, 23, 5, 4
- 1, 24, 3, 5
- 1, 24, 5, 3
- 1, 25, 3, 4
- 1, 25, 4, 3
- 2, 31, 4, 5
- 2, 31, 5, 4
- 2, 34, 1, 5
- 2, 34, 5, 1
- 2, 35, 1, 4
- 2, 35, 4, 1
- 3, 41, 2, 5
- 3, 41, 5, 2
- 3, 42, 1, 5
- 3, 42, 5, 1
- 3, 45, 1, 2
- 3, 45, 2, 1
- 4, 51, 2, 3
- 4, 51, 3, 2
- 4, 52, 1, 3
- 4, 52, 3, 1
- 4, 53, 1, 2
- 4, 53, 2, 1
- 5, 12, 3, 4
- 5, 12, 4, 3
- 5, 13, 2, 4
- 5, 13, 4, 2
- 5, 14, 2, 3
- 5, 14, 3, 2
These combinations cover all possible ways to follow the pattern of combining digits while following the sequence constraints.
Would you like more details or have any questions?
Here are 5 relative questions for further exploration:
- What would happen if the sequence involved 5 digits instead of 4?
- How would the solution change if the digits could repeat?
- Can we calculate the total number of possible sequences mathematically?
- What if the combined digits needed to appear at the end instead of the middle?
- How would the solution change if the digits had to follow a specific order (e.g., ascending)?
Tip: When working with sequences or combinations, it's often helpful to use tree diagrams to visualize all possibilities easily!
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Permutations
Sequences
Formulas
Permutation formula: P(n, r) = n! / (n - r)!
Theorems
Basic principles of permutations and combinations
Suitable Grade Level
Grades 6-8
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