Math Problem Statement
i am a 3 digit number the sum of my first two digits is 6 and the difference between my last two is zero my second digits is one half of my first and third i am 3 of a kind what am i
Solution
Let's carefully analyze the puzzle step by step:
Key Clues:
- Three-digit number: The number is in the form , where , , and are digits.
- The sum of the first two digits is 6: This gives us the equation .
- The difference between the last two digits is zero: This means .
- The second digit is one half of the first and third: This means .
- The number is 3 of a kind: All the digits must be equal.
Step-by-Step Solution:
We need to solve for the digits , , and , given the constraints:
- ,
- ,
- .
Since , substitute this into :
Multiply the entire equation by 2 to eliminate the fraction:
Now that we know , we can substitute it back into to find :
Since , we have .
Conclusion:
The three-digit number is 422.
Would you like more details, or do you have any questions?
Here are 5 questions to explore further:
- What if the sum of the first two digits was 7 instead of 6?
- Can you form a different puzzle with similar rules but a different number?
- How would this puzzle change if the second digit was twice the first digit instead of half?
- Can this problem be solved using a different method, like guessing and checking?
- What is the importance of carefully interpreting the given conditions in puzzles?
Tip: When solving puzzles, always write down each clue and convert them into equations or inequalities. This systematic approach will help you stay organized and avoid errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Basic Arithmetic
Equation Solving
Formulas
a + b = 6
b = c
b = a / 2
Theorems
-
Suitable Grade Level
Grades 6-8
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