## Problem of the Day #425: The Great ArkJanuary 1, 2013

Posted by Saketh in : potd , trackback

In anticipation of the end of the world a couple of weeks ago, Dasith constructed a giant ark to be filled with pairs of many different kinds of animals.

To avoid things getting messy on the ark, he had all of the animals order themselves in a single queue. He required the $i^{\textrm{th}}$ pair of animals to place themselves in the queue such that they were separated by exactly $i$ other animals.

Here is an example of such an arrangement, known as a Langford pairing:

Let $n$ be the total number of pairs of animals. The given example has $n=4$. Determine all values of $n$ for which a Langford pairing exists.