lieve there is a small typo in the formula for
  \( c \).  It should be \( c = 4x - 1 \).
</p>
<p>
  I found another blog post that references your post:
  <a href="https://vamshij.com/blog/linear-optimization/langford-problem/">https://vamshij.com/blog/linear-optimization/langford-problem/</a>.
</p>
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<!-- name: Susam Pal -->
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<p>
  Thank you, Ikiatl and Presh, for your comments.  The formula for \(
  c \) indeed had a typo.  Although I