Stone Game III (Strange Rules)

A subtractive game with a custom set of moves. The simple patterns are gone; can you find the new path to victory? This introduces Sprague-Grundy theorem concepts.

The Rules Have Changed

Background: Sprague-Grundy Theorem

Welcome to a more advanced impartial game. In this puzzle, the allowed moves are restricted to a specific set. This type of game is solved with the powerful **Sprague-Grundy Theorem**, which states that every impartial game under the normal play convention is equivalent to a Nim pile of a certain size. This size is called the Grundy value (g-value).

The AI has returned, but this time it has changed the rules. You can no longer take any number of stones you wish. You must choose from a specific set of moves. The game seems chaotic, but a hidden logic remains. Can you feel your way to victory?