text: ## Monday, May 14, 2012
  
  ### Visiting each of a number of points on a circle
  
  For twelve points on the circle you can move 5 steps around each time and visit every point once and end up back where you started. This is because if the points are labeled 1 through 12:
  (5*n+1) mod 12: n=0..12 = [1,6,11,4,9,2,7,12,5,10,3,8,1]
  
  For 14 points 5 works as well:
  (5*n+1) mod 14: n=0..14 = [1,6,11,2,7,12,3,8,13,4,9,14,5,10,1]
  
  For 16 points:
  (5*n+1) mod 16: n=0..16 = [1,6,11,16,5,10,15,4,9,14,3,8,13,2,7,12,1]
  
  20:
  (5*n+1) mod 20: n=0..20 = [1,6,11,16,1x
  
  So maybe it always happens when they don't share a factor:
  For 14:
  (3*n+1) mod 14: n=0..14 = [1,4,7,10,13,2,5,8,11,14,3,6,9,12,1]
  
  but (6*n+1) mod 14: n=0..14=[1,7,13,5,11,3,9,1x
  
  So my conjecture is this type of drawing can be made when:
  (s*n+1) mod C: n= 0..C = [every possible remainder once then repeat]
  for s and C coprime.
explanation: The document discusses a mathematical problem involving visiting each of a number of points on a circle by moving a fixed number of steps each time. It provides examples for different numbers of points (12, 14, 16, and 20) and explores the conditions under which all points are visited exactly once before repeating. The text concludes with a conjecture that this can be achieved when the step size and the number of points are coprime.
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: ## Monday, May 14, 2012
  
  ### Visiting each of a number of points on a circle
  
  For twelve points on the circle you can move 5 steps around each time and visit every point once and end up back where you started. This is because if the points are labeled 1 through 12:
  (5*n+1) mod 12: n=0..12 = [1,6,11,4,9,2,7,12,5,10,3,8,1]
  
  For 14 points 5 works as well:
  (5*n+1) mod 14: n=0..14 = [1,6,11,2,7,12,3,8,13,4,9,14,5,10,1]
  
  For 16 points:
  (5*n+1) mod 16: n=0..16 = [1,6,11,16,5,10,15,4,9,14,3,8,13,2,7,12,1]
  
  20:
  (5*n+1) mod 20: n=0..20 = [1,6,11,16,1x
  
  So maybe it always happens when they don't share a factor:
  For 14:
  (3*n+1) mod 14: n=0..14 = [1,4,7,10,13,2,5,8,11,14,3,6,9,12,1]
  
  but (6*n+1) mod 14: n=0..14=[1,7,13,5,11,3,9,1x
  
  So my conjecture is this type of drawing can be made when:
  (s*n+1) mod C: n= 0..C = [every possible remainder once then repeat]
  for s and C coprime.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document discusses a mathematical problem involving visiting each of a number of points on a circle by moving a fixed number of steps each time. It provides examples for different numbers of points (12, 14, 16, and 20) and explores the conditions under which all points are visited exactly once before repeating. The text concludes with a conjecture that this can be achieved when the step size and the number of points are coprime.
  
  Label: question-and-answer