text: 1. ## Making numbers add up to square numbers
  
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a line of a triangle that will add up to a square number.
  
  e.g. a
  b c
  
  a&b have to add up to a square, as well as a&c and b&c.
  
  Any help would be appreciated.
  
  Can anyone help?
  
  2. Originally Posted by Markdevs
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a triangle that will add up to a square number.
  
  Can anyone help?
  you may want to be a little more specific than that
  
  3. Originally Posted by Markdevs
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a line of a triangle that will add up to a square number.
  
  e.g. a
  b c
  
  a&b have to add up to a square, as well as a&c and b&c.
  
  Any help would be appreciated.
  
  Can anyone help?
  Do you mean like
  Code:
    -1
  2    2
  Or is there some restriction on the numbers a, b, c?
  
  -Dan
  
  4. Originally Posted by Markdevs
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a line of a triangle that will add up to a square number.
  
  e.g. a
  b c
  
  a&b have to add up to a square, as well as a&c and b&c.
  
  Any help would be appreciated.
  
  Can anyone help?
  Code:
     a
  b    c
  such that
  $\displaystyle a + b = x^2$
  
  $\displaystyle a + c = y^2$
  
  $\displaystyle b + c = z^2$
  
  Subtracting the first two equations gives me
  $\displaystyle a - c = x^2 - y^2$
  
  Adding this equation to the third equation give me
  $\displaystyle 2b = x^2 - y^2 + z^2$
  
  Thus
  $\displaystyle b = \frac{x^2 - y^2 + z^2}{2}$
  
  $\displaystyle c = z^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{-x^2 + y^2 + z^2}{2}$
  
  $\displaystyle a = x^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{x^2 + y^2 - z^2}{2}$
  
  You can pick any numbers x, y, z that you like.
  
  For example, letting x = 1, y = 2, and z = 3 gives
  Code:
     -2
  3    6
  -Dan
  
  EDIT: I can show that at least one of a, b, and c must be negative.
explanation: The document is a forum thread where a user named Markdevs posts a math question about arranging numbers in a triangle such that the sums of the numbers in each pair add up to a square number. The user provides an example and asks for help. Another user, Dan, responds with a detailed solution, providing a general formula for finding such numbers and an example.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 1. ## Making numbers add up to square numbers
  
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a line of a triangle that will add up to a square number.
  
  e.g. a
  b c
  
  a&b have to add up to a square, as well as a&c and b&c.
  
  Any help would be appreciated.
  
  Can anyone help?
  
  2. Originally Posted by Markdevs
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a triangle that will add up to a square number.
  
  Can anyone help?
  you may want to be a little more specific than that
  
  3. Originally Posted by Markdevs
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a line of a triangle that will add up to a square number.
  
  e.g. a
  b c
  
  a&b have to add up to a square, as well as a&c and b&c.
  
  Any help would be appreciated.
  
  Can anyone help?
  Do you mean like
  Code:
    -1
  2    2
  Or is there some restriction on the numbers a, b, c?
  
  -Dan
  
  4. Originally Posted by Markdevs
  Hi everyone,
  
  I'm stuck on this question and it's driving me crazy!!
  
  Basically you have to add numbers in a line of a triangle that will add up to a square number.
  
  e.g. a
  b c
  
  a&b have to add up to a square, as well as a&c and b&c.
  
  Any help would be appreciated.
  
  Can anyone help?
  Code:
     a
  b    c
  such that
  $\displaystyle a + b = x^2$
  
  $\displaystyle a + c = y^2$
  
  $\displaystyle b + c = z^2$
  
  Subtracting the first two equations gives me
  $\displaystyle a - c = x^2 - y^2$
  
  Adding this equation to the third equation give me
  $\displaystyle 2b = x^2 - y^2 + z^2$
  
  Thus
  $\displaystyle b = \frac{x^2 - y^2 + z^2}{2}$
  
  $\displaystyle c = z^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{-x^2 + y^2 + z^2}{2}$
  
  $\displaystyle a = x^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{x^2 + y^2 - z^2}{2}$
  
  You can pick any numbers x, y, z that you like.
  
  For example, letting x = 1, y = 2, and z = 3 gives
  Code:
     -2
  3    6
  -Dan
  
  EDIT: I can show that at least one of a, b, and c must be negative.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum thread where a user named Markdevs posts a math question about arranging numbers in a triangle such that the sums of the numbers in each pair add up to a square number. The user provides an example and asks for help. Another user, Dan, responds with a detailed solution, providing a general formula for finding such numbers and an example.
  
  Label: question-and-answer