Project Euler Forum

Presumably, a player loses if they don't have any available moves to play? I don't think this is mentioned explicitly.

Correct. That's pretty standard with combinatorial games - the winner is the last person to make a move; the loser is the first person who is unable to move for whatever reason. The alternative to this "normal play condition" is a misère game, where the first player unable to move wins, but that's less common. I don't think there's been a PE problem in CGT operating by misère rules, but I could be forgetting a case.

Maybe https://projecteuler.net/problem=400 is one with misère game ?

Is it permissible to remove the leading 1 from 101 to make it 1?
I sensed two possible interpretations from the statement “Leading zeros are not allowed in any ternary expansion”:
* Case 1: Since leading 0s are not allowed, transitioning from 101 to 01 is not permitted.
* Case 2: Since leading 0s are not allowed, removing the leading 1 from 101 causes an immediate transition to 1.

Yes, it is possible to remove such a 1. It will do 101 → 1.