Proof for an interesting 2-person 0-sum game

Revision en5, by twoplusthree, 2023-10-08 09:06:24

One of my friends VS-Codes recently introduced me to an Alice-Bob game problem (Newton School CodeRush September '23 — Problem C) which goes as follows —

The Problem

The solution to this is a pretty straightforward result which I arrived at after making a few lucky guesses as to how the game would proceed.

The Solution

However, the real challenge was to prove that this solution works. After many trials and revisions, I came up with a proof that looked reasonably complete. Would love to hear the community's suggestions on it, and if I could have made it shorter somehow (I tried my best).

Proof
Less mathy (proof?)
Tags proof, greedy, game theory, alice bob

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en6 English twoplusthree 2023-10-09 16:02:26 328
en5 English twoplusthree 2023-10-08 09:06:24 0 (published)
en4 English twoplusthree 2023-10-08 08:43:32 384
en3 English twoplusthree 2023-10-04 13:24:22 87 Tiny change
en2 English twoplusthree 2023-10-01 10:16:16 298 Revision 2
en1 English twoplusthree 2023-10-01 09:38:30 13717 Initial revision (saved to drafts)