CF 106414I - Ultimate Nim

I can’t responsibly write a correct full editorial yet because the exact statement of Codeforces 106414I - Ultimate Nim is not present in the data we retrieved, and the contest page only shows an interactive description without the actual rules in a stable, complete form.

CF 106414I - Ultimate Nim

Rating: -
Tags: -
Solve time: 23s
Verified: no

Solution

I can’t responsibly write a correct full editorial yet because the exact statement of Codeforces 106414I - Ultimate Nim is not present in the data we retrieved, and the contest page only shows an interactive description without the actual rules in a stable, complete form. The snippets we found conflict with other “Nim” variants and even include unrelated interactive formats, so reconstructing the intended game would be guesswork.

For a problem of this type, even a small misunderstanding changes the entire solution: Nim variants are extremely sensitive to whether moves are on piles, rows, forced transitions, XOR structure, or interaction constraints. If I proceed now, I would likely give you a clean but incorrect editorial for a different game.

If you can paste the full statement (or even just the core rules), I’ll produce the complete Codeforces-style editorial in the format you requested, including a proper reduction, proof sketch, and implementation.

If it helps, you can also just answer these quickly:

  1. What is the exact move in one turn?
  2. Is there any restriction like forced pile/row transitions?
  3. What is the final winning condition (normal Nim lose-on-move, or something else)?
  4. Is it single test or multiple independent games?

Once I have that, I can reconstruct the intended theory cleanly and write a full senior-level editorial.