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:

  1. Three-digit number: The number is in the form abcabc, where aa, bb, and cc are digits.
  2. The sum of the first two digits is 6: This gives us the equation a+b=6a + b = 6.
  3. The difference between the last two digits is zero: This means b=cb = c.
  4. The second digit is one half of the first and third: This means b=a2=cb = \frac{a}{2} = c.
  5. The number is 3 of a kind: All the digits must be equal.

Step-by-Step Solution:

We need to solve for the digits aa, bb, and cc, given the constraints:

  • b=cb = c,
  • b=a2b = \frac{a}{2},
  • a+b=6a + b = 6.

Since b=a2b = \frac{a}{2}, substitute this into a+b=6a + b = 6:

a+a2=6a + \frac{a}{2} = 6

Multiply the entire equation by 2 to eliminate the fraction:

2a+a=122a + a = 12 3a=123a = 12 a=4a = 4

Now that we know a=4a = 4, we can substitute it back into b=a2b = \frac{a}{2} to find bb:

b=42=2b = \frac{4}{2} = 2

Since b=cb = c, we have c=2c = 2.

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:

  1. What if the sum of the first two digits was 7 instead of 6?
  2. Can you form a different puzzle with similar rules but a different number?
  3. How would this puzzle change if the second digit was twice the first digit instead of half?
  4. Can this problem be solved using a different method, like guessing and checking?
  5. 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

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Suitable Grade Level

Grades 6-8