I like this one:

• covers every case where the total number of names could be different from the example (len(names) != 5)
• once you figure out the indices it works very intuitively to the "story" without a lot of thought paid to mathematics or other tricks; with only a few comments, you could actually re-tell the story that this solves
• it is also reasonably efficient, since a list is not utilized that may grow out of bounds
• this scales decently well too; we split the chance of integer overflow across everyone in the queue, effectively mitigating the chance by the number of unique people in the queue

Overall, not optimal but straightforward.

In retrospect:

• The range function is unneeded, as we could just use a blank hash-table/object to start out with and have the code assume all values are 0 if undefined.
• I could have collapsed variable initialization onto each other for common values.
• I could have dropped the "this" from the variables in exchange for closured vars in order to make the internal values 'private' to the function; although the starting status of the code suggest to use the "this.var = value" format explicitly.

Jaden deleted his twitter, so the flavor link is no longer valid. :(
https://twitter.com/officialjaden