The solution to today’s puzzle

Earlier today I set the following puzzle, a pre-commemoration of World Logic Day on January 14. Here it is again with the solution.

Middle management

Andy, Bea, and Celine have a jar of ten cookies. They will take turns putting their hands in the jar to take out cookies for themselves. Andy is first, then Bea, then Celine. On each turn, they can take as many as they like.

They agree to the following conditions: