I loved your blog post. It is the only convincing explanation and the best explanation that I could find on the web. If I write a blog post about this topic in the near future, I would definitely add a link to your post. Really great work!

Wonderful post! I am preparing a video on Langford pairings and your proof was incredibly helpful and written in great detail. Many articles come to the necessary condition and just assume sufficiency which is wrong. Yours is the only article that proves both the necessity and the sufficiency of the condition. The construction of the sequence in your post is wonderful.

I found another blog post that references your post: https://vamshij.com/blog/linear-optimization/langford-problem/.

Thank you, Ikiatl and Presh, for your comments. The formula for \( c \) indeed had a typo. Although I wrote the correct values for \( c \) obtained from the formula \( c = 4x - 1 \) in the examples, the formula itself was written incorrectly as \( c = 4x - 3 \). I have corrected this to \( c = 4x - 1 \) now. Also, thank you both for your kind words about this post!