Alice and Charlie play a game, taking turns with Alice going first.
A three-digit number n is written on a blackboard.
Move: Choose a non-zero digit k of n, and replace n with n − k.
Winning condition: The player who writes 100 on the blackboard wins.
If the starting number is 125, prove that Alice can always win. State Alice's first move and describe how Alice responds to any move Charlie makes.
Find, with proof, all three-digit starting values for which Charlie (the second player) has a winning strategy.
From UKMT Maclaurin Mathematical Olympiad 2025, Problem 2
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