Maximus is one of 3 or more prisoners of war who have been lined up before the Roman Emperor. The prisoners are numbered from first in the line to last as 1, 2, 3, 4, ..., N. The Emperor orders the execution of the prisoners in the following manner:

1) The first and last are immediately executed.
2) If there are still 2 or more prisoners remaining, the half of the remaining prisoners with the lowest numbers (rounded up) are executed.
3) If there are still 3 or more prisoners remaining, start again from Step 1.

For example, if there were 5 prisoners to start then prisoners 1 and 5 would be executed in Step 2, and prisoners 2 and 3 would be executed in Step 3, leaving prisoner 4 alive.

Is there a strategy by which Maximus can save himself? What if Maximus also wants to save his friend Romulus?

(In reply to Clarification? by Kenny M)

Sorry about this. I saw that people in the queue wanted to move the original Step 1 to the first paragraph. I renumbered the steps, but forgot to change the paragraph below. This is the second time in a row that I have made a mistake when doing a Scholar edit and pushing the problem. In the puzzle about the Well-known French name, I saw that the L*** was wrong. I accidentally made it L**** instead of moving it one space. Sorry.

Posted by Math Man on 2024-04-21 21:09:19