Sort:  

If you start on the most eastern island west of the dateline, and you move to the most western island east of the dateline within a certain period of time, you can experience a 51-hour day.
https://www.timeanddate.com/time/map/

Oh that's interesting!

It's just incredibly difficult to imagine.
You need to cross three timezones. A timezone is 15 degrees, so you would have to move 45 degrees west. You start where the day starts, February 1 for example. The day already started in Kiribati. It is now 6 pm UTC on January 31. In Kiribati it's 8 am, Wednesday, Feb 1. So if you started there 8 hours ago, you may have to cross the dateline at exactly midnight, I'm not sure about that. So during the night the date will still be February 1, until you end on Guam or the Northern Mariana islands, I don't know exactly which one, where the day ends, 51 hours after it started.
Edit: The day ends at Attu Island. Which I should have known, because I have been looking around there, looking for an island to send our perceived leaders to. I figured we could drop them on Agattu Island, which is one island east of Attu Island.

And I like to dig into unfinished past conversations.
The 26 hour days you mentioned did not get through to me the first time I read your comment. I was focused on the 51-hour day. So, reading it again, now that you mention it, 26 hour days? Wow!
How would that work? After the first day, the next day would start at 2 am. The third day starts at 4 am. The thirteenth day starts at 0:00 am. So, he must have lived 13 days every two weeks.
A week is 168 hours. I just happen to know that. So two weeks is 336 hours.
13 times 26 hours? Is 338 hours. That's unfortunate. It's more complicated than 13 days per two weeks.
He lived in periods of 13 days. He lived 12 days every 13 day period.
365¼ divided by 13 makes 28.1. It makes no sense to me.