Math Problem Statement
make the sums of 2-digit sets use all 6 available numbers in both the sum and the result without repeating
Solution
To solve this problem, let's break it down into a step-by-step process.
Objective:
- Create two 2-digit numbers that sum up to another 2-digit number.
- Use all 6 digits from the two numbers and the result without repeating any digits.
Step-by-Step Process:
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Identify the set of digits: We need to find a set of 6 digits that can be split into two 2-digit numbers and their sum without repeating any digits.
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Example Attempts: Let's try different combinations and verify the results.
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Example 1:
- Two 2-digit numbers: 29 + 48
- Sum: 77
- Used digits: 2, 9, 4, 8, 7, 7
- Problem: The digit 7 repeats, so this set does not satisfy the condition.
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Example 2:
- Two 2-digit numbers: 36 + 47
- Sum: 83
- Used digits: 3, 6, 4, 7, 8, 3
- Problem: The digit 3 repeats, so this set does not satisfy the condition.
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Example 3:
- Two 2-digit numbers: 19 + 37
- Sum: 56
- Used digits: 1, 9, 3, 7, 5, 6
- Solution: No digits repeat! This set satisfies the condition.
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Solution:
- Numbers: 19 + 37 = 56
- Used Digits: 1, 9, 3, 7, 5, 6
- All digits are used once, and the sum is correct.
Would you like to explore another example, or do you have any questions?
Here are five questions to consider:
- Can you identify other 2-digit combinations that meet the same criteria?
- What is the significance of the digit sum when creating these sets?
- How might the problem change if three 2-digit numbers were involved instead of two?
- What strategy would you use to ensure all digits are unique in future sums?
- How would the problem complexity increase with larger digit sets?
Tip: When working with sums and digit constraints, always check the result early on to ensure no digit repetition. This saves time on testing combinations.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Sum of Digits
Combinatorics
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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