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Problem of the Month (January 2017)

A Langford List is a list of numbers, each appearing twice, so that the number of the numbers in between the occurrences of n is n. The smallest such example is 4 1 3 1 2 4 3 2. Define a Language Langford List to be a list of spellings of positive integers, each appearing twice, so that there are exactly n letters between the two occurrences of the number n. What is the smallest Langford List containing a given number? We can also do this in two dimensions. What is the smallest Language Langford Array containing a given number?

We can also use different counting systems. For each positive number, what is this shortest Roman Numeral Langford List, where the number of line segments between two numbers are counted? Or the shortest Digital Clock Langford List, where the number of LED segments between the two numbers are counted? Or the shortest Coinage Langford List, where the smallest number of US coins to represent that many cents are counted?


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