Can the pattern of 312132 and 23421314 be continued: numbers made of pairs of each digit 1..n, with the two...

combinatorics/langford New, unsolved

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Can the pattern of 312132 and 23421314 be continued: numbers made of
pairs of each digit 1..n, with the two k's separated by k digits?

Three pairs number: 3s separated by 3 digits; 2s separated by 2 digits;
1s separated by 1 digit.
312132

I was playing with these numbers and made a 4 pairs number: 4s
separated by 4 digits; 3s separated by 3 digits; 2s separated by 2
digits; 1s separated by 1 digit.
23421314

I wonder if this pattern could go on?

-- Jan Merolant <jan.merolant@club.tip.gov>

[ Editor: the first paragraph is the editor's summary. ]

Show solution

No solution was found in the collected postings.

This question is known as "Langford's Problem".  An excellent web page
on it and some related questions is
http://www.lclark.edu/~miller/langford.html .

-- Fred W. Helenius <fredh@ix.netcom.com>