title: Strategy with regard to how to approach this algorithm?
body: <p>I was asked this question in a test and I need help with regards to how I should approach the solution, not the actual answer. The question is</p>
  <blockquote>
  <p>You have been given a 7 digit number(with each digit being distinct and 0-9). The number has this property</p>
  <p>product of first 3 digits = product of last 3 digits = product of central 3 digits</p>
  </blockquote>
  <p>Identify the middle digit.</p>
  <p>Now, I can do this on paper by brute force(trial and error), the product is 72 and digits being</p>
  <blockquote>
  <p>8,1,9,2,4,3,6</p>
  </blockquote>
  <p>Now how do I approach the problem in a no brute force way?</p>