Langford's Problem

This is a Langford sequence, closely-related to the Skolem sequence:

312132

Here's a challenge, can you spot the pattern that makes it a Langford sequence?

Hint

Solution

The answer is that for the sequence 312132, there is one number between the pair of 1s, two numbers between the pair of 2s and three numbers between the pair of 3s. The sequence 41312432 extends this pattern to include 4. In the Math section we explore extending these types of sequences to larger numbers. For now, it's time to learn about Skolem sequences!