That what I was thinking.

Comments would have been nice, however, this is a great solution in my opinion. Especially when compared to the monstrosity I came up with. I am somewhat of a newbie and I could understand the solution. When I see a solution like this I wonder what my mind does during the process of determining the best way to work this.

Some problems are inherently mathematical. And often, a mathematical solution is necessary, otherwise the computation is intractable. You might like to know that computers were basically invented to solve mathematical problems that had undergone 'mathematical transformations'.

Oops, right. I wasn't sure my solution would always work, but I trusted the test cases (am in no way proficient in maths).

If I understand the Kata correctly, item_index itself is also a zero based index, so:

item_indexes 0, 1, 2, 3 should return 0
item_index 4 should return 1

The other solutions are extremely slow so this would definitely be the best way to solve it if it was part of a bigger program.

This solution was for Python 2, and valid at that time.