Strange Nim Game

Alice and Bob are playing a strange variant of the Nim game. The rules are as follows: 1. There are $N$ towers, with the $i$-th tower having $A_i$ rings. 2. On their turn, a player selects a tower $i$ that contains a positive number of rings, and a **positive** digit $d$ such that $d$ appears in the decimal representation of $A_i$. Then, they remove $d$ rings from the $i$-th tower. - For exa