Math Problem Statement
Solution
To solve this problem, we need to find three more three-digit numbers that satisfy the given conditions:
- The digits , , and are all different.
- The product is equal to the two-digit number represented by , which we interpret as .
The example given, , meets these conditions because:
- The digits , , and are all different.
- The product , which matches the two-digit number (from ).
Steps to find the remaining numbers
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Test Possible Values for , , and : We need , , and such that: We will test combinations with , , and being different digits from 1 to 9, and ensure that yields a two-digit number .
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List Potential Solutions: By systematically testing possible values, we look for cases where both conditions hold.
Solution Verification
After testing different combinations, here are the values that satisfy both conditions:
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: , ,
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: , ,
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: , ,
Thus, Norbert's four favorite numbers are:
Would you like a detailed breakdown of the solution steps, or have further questions?
Related Questions:
- What other sets of numbers could satisfy similar conditions with different constraints?
- How would the solution change if the product had to be a three-digit number?
- Can this problem be solved using an algebraic approach rather than testing cases?
- What mathematical principles are used in solving this kind of problem?
- How does changing the base (e.g., base 8) affect the solution?
Tip:
When faced with digit constraints in problems, check systematically and carefully to avoid missing valid cases.
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Math Problem Analysis
Mathematical Concepts
Multiplication
Digit Manipulation
Properties of Numbers
Formulas
A × B × C = 10B + C
Theorems
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Suitable Grade Level
Grades 5-7
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