title: How to approach 'four points, two distance, unique shapes' problem, computationally
body: <p>Looking for a way to find solutions for this problem computationally (using program) without pen and paper or plotting.</p>
  
  <p>Find all the ways to arrange four points so that only two distances occur between any two points</p>
  
  <p>In other words, how many ways are there to draw four dots on a piece of paper such that whichever two dots you choose, the distance between these two points is one of two values?</p>
  
  <p>Source : <a href="https://www.theguardian.com/science/series/alex-bellos-monday-puzzle" rel="nofollow noreferrer">https://www.theguardian.com/science/series/alex-bellos-monday-puzzle</a></p>
  
  <p><a href="https://i.stack.imgur.com/dbvEK.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/dbvEK.png" alt="Solutions that satisfy "></a></p>
  
  <p>Edit 1: Not looking for the solutions themselves. Looking for the computational approach (formal approach) to arrive at the solution.</p>